Wavefunction-based quantum-chemicalab initiocalculations for core electron binding energies of small open shell molecules.

Core electron binding energies (CEBEs), i.e. ionization energies of 1s core orbitals, are calculated by means of wavefunction-based quantum-chemicalab initiomethods for a series of small open-shell molecules containing first-row atoms. The calculations are performed in three steps: (a) Koopmans' theorem, where the orbitals of the electronic ground state are used unchanged also for the ions, (b) Hartree-Fock or self consistent field (SCF) approximation in which the orbitals are allowed to relax after 1s ionization (ΔSCF), (c) dynamic correlation effects on top of SCF. For open-shell molecules 1s ionization leads to ions in several spin states, mostly to a pair of a triplet and a singlet state. In several cases one or both of these ionic states are only poorly described by a single-reference SCF wavefunction, therefore a multi-reference complete active space self consistent field (CAS-SCF) wavefunction is used instead. The correlation effects are evaluated by means of our multi-reference coupled electron pair approximation program. The accuracy of the calculated CEBEs is in the order of 0.1-0.4 eV. This is in agreement with experimental results for NO and O2. But there exist only very few gas phase data for CEBEs of open-shell molecules.

ESCAPE: A novel approach for a fast estimation of dynamic correlation energies: Application to large organic molecules.

Advanced wave function-based quantum chemical ab initio methods, such as CCSD(T), are able to calculate the energies of small- to medium-sized molecules with chemical accuracy. Unfortunately, these methods scale quite unfavorably with the size of the system and are getting too time consuming-and too expensive-for larger molecules. In order to be able to treat larger organic molecules, we propose a novel scheme for a quick and reliable estimate of molecular correlation energies, which we call ESCAPE (EStimation of CorrelAtion energies by Pair Energies). It is based on the pair correlation energies for localized molecular orbitals that have been generated by CCSD[T] and fitted to suitable functional forms. All fit parameters are stored in a large parameter file. Aiming at chemical accuracy (±1 kcal/mol), we have first limited our approach to aliphatic hydrocarbons. The total molecular CCSD[T] correlation energies of a training set of 41 aliphatic hydrocarbons could be reproduced with a mean absolute error (MAE) of 0.56 kcal/mol or 0.11%. A similar accuracy could be obtained for a test set of 11 additional hydrocarbons with up to eight carbon atoms (MAE of 0.65 kcal/mol or 0.09%). In a more critical test, we checked the small energy differences for a set of 13 isomerization reactions. The comparison with experimental data showed that we could reach chemical accuracy as well. Our estimate (MAE of 0.55 kcal/mol) is slightly inferior to the CCSD[T] result (MAE of 0.17 kcal/mol), but superior to SCF, DFT/B3LYP, and DFT/B3LYP + D3. Moreover, in all cases, we obtained the correct sign, that is, the correct equilibrium structure. A similar accuracy could be reached in an application to the three lowest isomers of the C60 molecule. Using the example of a set of eight alcohols, we were able to proof the method's ability for molecules including heteroatoms. Three fast steps are necessary for the application to any aliphatic hydrocarbon or alcohol: (1) An SCF calculation at the selected molecular geometry; it can be fast since a medium size basis set is generally sufficient. (2) The localization of the occupied molecular orbitals and determination of their properties (center of charge and spatial extent). (3) Estimate of the correlation energy using the existing parameter file. © 2019 Wiley Periodicals, Inc.

Vibrational Action Spectroscopy of Solids: New Surface-Sensitive Technique.

Vibrational action spectroscopy employing infrared radiation from a free-electron laser has been successfully used for many years to study the vibrational and structural properties of gas phase aggregates. Despite the high sensitivity of this method no relevant studies have yet been conducted for solid sample surfaces. We have set up an experiment for the application of this method to such targets, using infrared light from the free-electron laser of the Fritz Haber Institute. In this Letter, we present first results of this technique with adsorbed argon and neon atoms as messengers. We were able to detect surface-located vibrations of a thin V_{2}O_{3}(0001) film on Au(111) as well as adsorbate vibrations, demonstrating that this method is highly surface sensitive. We consider that the dominant channel for desorption of the messenger atoms is direct inharmonic vibrational coupling, which is essentially insensitive to subsurface or bulk vibrations. Another channel is thermal desorption due to sample heating by absorption of infrared light. The high surface sensitivity of the nonthermal channel and its insensitivity to subsurface modes makes this technique an ideal tool for the study of surface-located vibrations.

Magnetostructural dynamics of Rieske versus ferredoxin iron-sulfur cofactors.

The local chemical environment of the [2Fe-2S] cofactor hosted by ferredoxin and Rieske-type proteins is fundamentally different due to the presence of distinct ligands at the two iron centers in the case of Rieske proteins, whereas they are identical in ferredoxins. This renders Rieske [2Fe-2S] cores chemically asymmetric and results in more complex vibrational spectra as compared to ferredoxin. Likewise, one would expect other properties, for instance the dynamics of the magnetic exchange coupling constant J, to be also more complex. Applying ab initio molecular dynamics using our recently introduced spin-constrained two-determinant extended broken symmetry (CEBS) approach to Rieske and ferredoxin model complexes at 300 K, we extract the molecular fluctuations and the resulting magnetostructural cross-correlations involving the antiferromagnetic exchange interaction J(t). This analysis demonstrates that the details of the magnetostructural dynamics are indeed distinctly different for Rieske and ferredoxin cofactors, while the time averages of 〈J〉 are shown to be essentially identical. In particular, the frequency window between about 200 and 350 cm(-1), is a "fingerprint region" that allows one to distinguish chemically asymmetric from symmetric cofactors and thus Rieske proteins from ferredoxins.

Surface core-level binding energy shifts for MgO(100).

Theoretical and experimental results for the surface core-level binding energy, BE, shifts, SCLS, for MgO(100) are presented and the anomalous O(1s) SCLS is interpreted in terms of the surface electronic structure. While the Mg(2p) surface BE shifts to a higher value than bulk by ≈1 eV as expected from the different surface and bulk Madelung potentials, the O(1s) SCLS is almost 0 rather than ≈-1 eV, expected from the Madelung potentials. The distortion of the surface atoms from the spherical symmetry of the bulk Mg and O atoms is examined by a novel theoretical procedure. The anomalous O SCLS is shown to arise from the increase of the effective size of surface O anions.

The iron-sulfur core in Rieske proteins is not symmetric.

At variance with ferredoxins, Rieske-type proteins contain a chemically asymmetric iron-sulfur cluster. Nevertheless, X-ray crystallography apparently finds their [2Fe-2S] cores to be structurally symmetric or very close to symmetric (i.e. the four iron-sulfur bonds in the [2Fe-2S] core are equidistant). Using a combination of advanced density-based approaches, including finite-temperature molecular dynamics to access thermal fluctuations and free-energy profiles, in conjunction with correlated wavefunction-based methods we clearly predict an asymmetric core structure. This reveals a fundamental and intrinsic difference within the iron-sulfur clusters hosted by Rieske proteins and ferredoxins and thus opens up a new dimension for the ongoing efforts in understanding the role of Rieske-type [2Fe-2S] cluster in electron transfer processes that occur in almost all biological systems.

Designing the Redox-Driven Switching of Ferro- to Antiferromagnetic Couplings in Organic Diradicals.

Switching of the magnetic exchange coupling from ferro- to antiferromagnetic or vice versa in a single molecule is an appealing but rarely occurring phenomenon in molecular magnetism. Here, we report this for an unprecedented pure organic system, computationally designed by tailoring a conformationally restricted, known nitroxide-diradical (Rajca et al. J. Am. Chem. Soc. 2007, 129, 10159). This ferro- to antiferromagnetic coupling switching of an "m-phenylene" based diradical is governed by a stereoelectronic effect and controlled by a redox-driven chemical reaction.

Ab initio calculation of correlation effects for the O 1s core electron binding energy in MgO.

Wavefunction based ab initio embedded cluster calculations are employed to calculate the O 1s core electron binding energies (CEBEs) of bulk MgO and the MgO(001) surface. A quantum cluster consisting of 61 atoms in five layers and embedded in a large point charge field is used for bulk MgO, the cluster for the MgO(001) surface is chosen accordingly. The O 1s CEBEs are calculated at the Koopmans' theorem (KT) and ΔSCF levels and with inclusion of correlation effects by means of the MC-CEPA method (multi-configuration coupled electron pair approximation), which is an approximate multi-reference coupled cluster approach. The correlation contributions to the O 1s CEBE of the central O atom due to the Mg atoms in the first and the O atoms in the second coordination shell turned out to be additive to a large extent. Therefore, they could be evaluated in an incremental fashion by a series of smaller calculations, where only a few atoms are included in the correlation treatment rather than all atoms of the first coordination shells or of the full quantum cluster. This makes the calculations feasible, even if large basis sets are used. The final results for the O 1s CEBEs are 533.47 and 533.50 eV for bulk MgO and the MgO(001) surface, to which electron correlation contributes 0.77 and 0.70 eV, respectively.

Constrained spin-density dynamics of an iron-sulfur complex: ferredoxin cofactor.

The computation of antiferromagnetic exchange coupling constants J by means of efficient density-based approaches requires in practice to take care of both spin projection to approximate the low spin ground state and proper localization of the magnetic orbitals at the transition metal centers. This is demonstrated here by a combined approach where the extended broken-symmetry (EBS) technique is employed to include the former aspect, while spin density constraints are applied to ensure the latter. This constrained EBS (CEBS) approach allows us to carry out ab initio molecular dynamics on a spin-projected low spin potential energy surface that is generated on-the-fly by propagating two coupled determinants and thereby accessing the antiferromagnetic coupling along the trajectory. When applied to the prototypical model of the oxidized [2Fe-2S] cofactor in Ferredoxins, [Fe(2)S(2)(SH)(4)](2-), at room temperature, CEBS leads to remarkably good results for geometrical structures and coupling constants J.

A theoretical study of the XP and NEXAFS spectra of alanine: gas phase molecule, crystal, and adsorbate at the ZnO(10 Ì 10) surface.

The adsorption of alanine on the mixed-terminated ZnO(10 ̅10) surface is studied by means of quantum-chemical ab initio calculations. Using a finite cluster model and the adsorption geometry as obtained both by periodic CPMD and embedded cluster calculations, the C1s, N1s and O1s X-ray photoelectron spectra (XPS) and near-edge X-ray absorption fine structure (NEXAFS) spectra are calculated for single alanine molecules on ZnO(10 ̅10). These spectra are compared with the spectra calculated for alanine in the gas phase and in its crystalline form and with experimental XPS and NEXAFS data for the isolated alanine molecule and for alanine adsorbed on ZnO(10 ̅10) at multilayer and monolayer coverage. The excellent agreement between the experimental and calculated XP and NEXAFS spectra confirms the calculated adsorption geometry: A single alanine molecule is bound to ZnO(10 ̅10) in a dissociated bidentate form with the two O atoms of the acid group bound to two Zn atoms of the surface and the proton transferred to one O atom of the surface. Other possible structures, such as adsorption of alanine in one of its neutral or zwitterionic forms in which the proton of the -COOH group remains at this group or is transferred to the amino group, can be excluded since they would give rise to quite different XP spectra. In the multilayer coverage regime, on the other hand, alanine is in its crystalline form as is also shown by the analysis of the XP spectra.

Method of local increments for the calculation of adsorption energies of atoms and small molecules on solid surfaces. 2. CO/MgO(001).

The method of local increments is used in connection with an embedded cluster approach and wave function based quantum chemical ab initio methods to describe the adsorption of a single CO molecule on the MgO(001) surface. The first step in this approach is a conventional Hartree-Fock calculation. The occupied orbitals are then localized by means of the Foster-Boys localization procedure, and the full system is decomposed into several "subunits" that consist of the orbitals localized at the CO molecule and at the Mg and O atoms of the MgO cluster. The correlation energy is expanded into a series of local n-body increments that are evaluated separately and independently. In this way, big savings in computer time can be achieved because (a) the treatment of a large system is replaced with a series of much faster calculations for small subsystems and (b) the big basis sets necessary for describing dispersion effects are only needed for the atoms in the respective subsystem while all other atoms can be treated by medium size Hartree-Fock type basis sets. The coupled electron pair approach, CEPA, an approximate coupled cluster method, is used to calculate the correlation energies of the various subsystems. For the vertical adsorption of CO on top a Mg atom of the MgO(001) surface with the C atom toward Mg, the individual one- and two-body increments are calculated as functions of the CO-MgO separation and a full potential energy curve is constructed from them. A very shallow minimum with an adsorption energy of 0.016 eV at a Mg-C distance of 3.04 Å is found at the Hartree-Fock level, while inclusion of correlation (dispersion) effects shortens the Mg-C distance to 2.59 Å and yields a much larger adsorption energy of 0.124 eV. This is in very good agreement with the best experimental value of 0.14 eV. The basis set superposition error, BSSE, was fully corrected for by the counterpoise method and the bonding mechanism was analyzed at the Hartree-Fock level by means of the constrained space orbital variation, CSOV, analysis.

Revealing the magnetostructural dynamics of [2Fe-2S] ferredoxins from reduced-dimensionality analysis of antiferromagnetic exchange coupling fluctuations.

Metalloproteins are biomolecular hybrids composed of an "inorganic core" embedded in a "bioorganic matrix". Cofactors typically contain transition metal clusters with complex electronic structure whereas the protein host undergoes dynamics on many length and time scales. This renders computational studies of spectroscopic properties challenging, in particular, when magnetic interactions are involved. In the present study we introduce a simplified description of the antiferromagnetic exchange coupling J in reduced dimensionality which allows one to study magnetostructural dynamics of [2Fe-2S] type iron-sulfur proteins in their oxidized form by molecular dynamics. It is demonstrated that parametrization in terms of a 2D J-surface faithfully reproduces the rigorous results both in vacuo and in Anabaena ferredoxin. In particular, we present a parametrization which relies on a spin-projected density functional approach based on two Kohn-Sham determinants corrected for self-interaction via a self-consistent linear-response Hubbard-U technique. This yields an average J for Anabaena Fd in close agreement with experimental in vitro results without any specific adjustment or fitting. The analytical J-surface can be used for [2Fe-2S] proteins in their oxidized form in general and the idea can be extended to other metalloproteins as well as to other spectroscopic properties.

Magnetostructural Dynamics from Hubbard-U Corrected Spin-Projection: [2Fe-2S] Complex in Ferredoxin.

A Hubbard-corrected spin-projected two-determinant approach, EBS+Uscf, is introduced to treat low-spin ground states of antiferromagnetically coupled transition metal complexes. In addition to providing access to total energies, forces, and ab initio simulations, it allows one to readily compute Heisenberg's exchange coupling J(t) on the fly. By studying the binuclear [2Fe-2S] cofactor in a metalloprotein, Anabaena Fd, within this consistent nonempirical procedure in combination with a QM/MM framework, it is illustrated that spin-projection, self-interaction corrections, thermal fluctuations, and protein matrix shifts are crucial in obtaining ⟨J⟩ close to the experiment.

The method of local increments for the calculation of adsorption energies of atoms and small molecules on solid surfaces. Part I. A single Cu atom on the polar surfaces of ZnO.

The method of local increments is used in connection with the supermolecule approach and an embedded cluster model to calculate the adsorption energy of single Cu atoms at different adsorption sites at the polar surfaces of ZnO. Hartree-Fock calculations for the full system, adsorbed atom and solid surface, and for the fragments are the first step in this approach. In the present study, restricted open-shell Hartree-Fock (ROHF) calculations are performed since the Cu atom possesses a singly-occupied 4s orbital. The occupied Hartree-Fock orbitals are then localized by means of the Foster-Boys localization procedure. The correlation energies are expanded into a series of many-body increments which are evaluated separately and independently. In this way, the very time-consuming treatment of large systems is replaced with a series of much faster calculations for small subunits. In the present application, these subunits consist of the orbitals localized at the different atoms. Three adsorption situations with rather different bonding characteristics have been studied: a Cu atom atop a threefold-coordinated O atom of an embedded Zn(4)O(4) cluster, a Cu atom in an O vacancy site at the O-terminated ZnO(000-1) surface, and a Cu atom in a Zn vacancy site at the Zn-terminated ZnO(0001) surface. The following properties are analyzed in detail: convergence of the many-body expansion, contributions of the different n-body increments to the adsorption energy, treatment of the singly-occupied orbital as "localized" or "delocalized". Big savings in computer time can be achieved by this approach, particularly if only the localized orbitals in the individual increment under consideration are described by a large correlation adapted basis set, while all other orbitals are treated by a medium-size Hartree-Fock-type basis set. In this way, the method of local increments is a powerful alternative to the widely used methods like DFT or RI-MP2.

Magnetostructural Dynamics with the Extended Broken Symmetry Formalism: Antiferromagnetic [2Fe-2S] Complexes.

A general spin-projection framework is laid out which allows one to perform ab initio molecular dynamics simulations of antiferromagnetically coupled spin dimers. The method extends the well-established broken-symmetry formalism and is systematically and consistently improvable. It allows for accessing structure within the same spin-projection approximation as employed to compute the exchange coupling constant J of such complexes in their low-spin state as a function of time. The resulting time evolution of the exchange coupling, J(t), can be analyzed most conveniently in terms of the corresponding power spectrum, J(ω), thus giving access to dynamical magnetostructural properties. The method has been implemented using a well-tested approximation to spin-projection and was applied to a minimal [2Fe-2S] model, i.e. to the [Fe2S2(SH)4](2-) complex at 300 K in vacuo. Thermal fluctuations at room temperature are found to change the antiferromagnetic coupling J by about 50% with respect to the average value, and the features of its power spectrum, J(ω), can be traced back to a coupling of J to particular vibrational modes.

Dynamical magnetostructural properties of Anabaena ferredoxin.

A mixed quantum/classical investigation of the dynamical magnetostructural properties, that is, "magnetodynamics," of oxidized Anabaena PCC7119 ferredoxin is carried out at room temperature in two distinct conformational states. This protein hosts a [2Fe-2S] cluster in which two iron centers are antiferromagnetically coupled to an overall low-spin electronic ground state that has a genuine multireference character. To study the magnetodynamics of this prosthetic group, an approximate spin projection method is formulated in the framework of density functional theory that allows for multideterminant ab initio molecular dynamics simulations to be carried out efficiently. By using this scheme, the influence of both thermal fluctuations and conformational motion on the structure of the [2Fe-2S] cluster and on the dynamics of the antiferromagnetic coupling constant, J(t), has been investigated. In addition to demonstrating how sensitively the shape of the [2Fe-2S] core itself is affected by hydrogen bonding, the analyses reveal a complex dynamical coupling of J to both local vibrations and large-amplitude motion. It is shown that this interplay can be understood in terms of specific vibrational modes and distinct hydrogen-bonding patterns between the iron-sulfur cluster and the protein backbone, respectively. This implies going beyond the Goodenough-Kanamori rules for angular magnetostructural correlations of oxidized iron-sulfur prosthetic groups.

Adsorption of benzene on coinage metals: a theoretical analysis using wavefunction-based methods.

The interaction of benzene with a Ag(111) surface has been determined using reliable ab initio electronic structure calculations. The results are compared to a recent detailed analysis of the interaction of benzene with copper and gold surfaces, thus making it possible to derive a consistent picture for the electronic structure changes encountered when benzene is brought into contact with the densely packed coinage metal surfaces. To avoid the problems encountered when the presently most frequently employed computational approach, density functional theory (DFT), is applied to adsorbate systems where dispersion (or van der Waals) forces contribute substantially, we use a wavefunction-based approach. In this approach, the weak van der Waals interactions, which are dominated by correlation effects, are described using second-order perturbation theory. The surface dipole moment and the work function changes induced upon adsorption are also discussed.

Ab initio calculations of the O1s XPS spectra of ZnO and Zn oxo compounds.

O1s core level binding energies of oxygen atoms in bulk ZnO, at different ZnO surfaces, and in some Zn oxo compounds were calculated by means of wave function based quantum chemical ab initio methods. Initial and final state effects were obtained by Koopmans' theorem and at the DeltaSCF level, respectively. After correction for scalar relativistic effects and electron correlation, the calculated XPS peak positions are in excellent agreement with the available experimental data for all systems included in the present study. The O1s core level shifts between an isolated H2O molecule and the Zn oxo compounds or ZnO, as well as between oxygen atoms in bulk ZnO and at various ZnO surfaces, can be understood by means of Madelung potentials and electronic relaxation or screening. XPS spectra were calculated for various cluster models which are designed to describe different possibilities of stabilizing the polar O-terminated ZnO(0001) surface by the adsorption of H atoms. The experimental spectra are only compatible with the theoretical results for the fully hydroxylated H-ZnO(0001) surface exhibiting a (1x1) surface structure.

Ab initio calculations for the Zn 2s and 2p core level binding energies in Zn oxo compounds and ZnO.

The Zn 2s and 2p core level binding energies of ZnO and a few Zn oxo compounds containing Zn in its oxidation state +2 were calculated by means of wave function based quantum chemical ab initio methods. The computations were performed at two levels of approximation. First, Hartree-Fock calculations were carried out for the ground state of the neutral systems yielding the "initial state" effects, i.e. the shifts of the core level binding energies due to the changes in the chemical environment of the Zn atom under consideration (Koopmans' theorem level, KT). In the second step, Hartree-Fock calculations were performed for the core ionized states in order to account for the relaxation effects after ionization, i.e. for the "final state" effects (DeltaSCF level). Scalar relativistic corrections and spin-orbit coupling were included in a "spin-orbit-coupling configuration interaction" (SOC-CI) treatment both at the KT and DeltaSCF levels. In all Zn oxo compounds (Zn(4)O(formate)(6), Zn(4)O(acetate)(6) and several ZnO cubanes) small negative initial state shifts between -1.0 and 0.0 eV (relative to the free Zn atom) were found which are caused by the negative charges at the surrounding O atoms. The relaxation effects vary between -1.0 and -0.5 eV, such that the calculated total shifts are moderately negative (-1.5 to -0.5 eV). Embedded ZnO clusters of increasing size, ranging from Zn(13)O(4) to Zn(69)O(38), were used as models for bulk ZnO, the Zn 2s and 2p core level shifts calculated for these clusters being extrapolated to infinite cluster size. The calculations show that bulk ZnO has a rather large negative initial state shift of -2.1 +/- 0.1 eV, due to the Madelung potential at the Zn atom, and a comparatively small relaxation contribution of -1.0 +/- 0.1 eV. This yields a total shift of -3.1 +/- 0.2 eV (both for 2s and 2p, relative to atomic Zn), which is in very good agreement with experiment, -2.9 +/- 0.2 eV. The surprising experimental observation that the Zn 2s and 2p XPS peak positions are nearly identical in Zn metal and ZnO is explained by the fact that the sum of initial and final state effects is accidentally the same for the two systems though the individual contributions differ quite significantly: the initial and final state shifts amount to +2.4 and -5.1 eV for Zn metal vs.-2.1 and -1.0 eV for ZnO.