Permutation symmetry in spin-adapted many-body wave functions

In the domain of exchange-coupled polynuclear transition-metal (PNTM) clusters, local emergent symmetries exist which can be exploited to greatly increase the sparsity of the configuration interaction (CI) eigensolutions of such systems. Sparsity of the CI secular problem is revealed by exploring the site permutation space within spin-adapted many-body bases, and highly compressed wave functions may arise by finding optimal site orderings. However, the factorial cost of searching through the permutation space remains a bottleneck for clusters with a large number of metal centers. In this work, we explore ways to reduce the factorial scaling, by combining permutation and point group symmetry arguments, and using commutation relations between cumulative partial spin and the Hamiltonian operators, . Certain site orderings lead to commuting operators, from which more sparse wave functions arise. Two graphical strategies will be discussed, one to rapidly evaluate the commutators of interest, and one in the form of a tree search algorithm to predict how many and which distinct site permutations are to be analyzed, eliminating redundancies in the permutation space. Particularly interesting is the case of the singlet spin states for which an additional reversal symmetry can be utilized to further reduce the number of distinct site permutations.

Resolution of Low-Energy States in Spin-Exchange Transition-Metal Clusters: Case Study of Singlet States in [Fe(III)4S4] Cubanes

Polynuclear transition-metal (PNTM) clusters owe their catalytic activity to numerous energetically low-lying spin states and stable oxidation states. The characterization of their electronic structure represents one of the greatest challenges of modern chemistry. We propose a theoretical framework that enables the resolution of targeted electronic states with ease and apply it to two [Fe(III)₄S₄] cubanes. Through direct access to their many-body wave functions, we identify important correlation mechanisms and their interplay with the geometrical distortions observed in these clusters, which are core properties in understanding their catalytic activity. The simulated magnetic coupling constants predicted by our strategy allow us to make qualitative connections between spin interactions and geometrical distortions, demonstrating its predictive power. Moreover, despite its simplicity, the strategy provides magnetic coupling constants in good agreement with the available experimental ones. The complexes are intrinsically frustrated anti-ferromagnets, and the obtained spin structures together with the geometrical distortions represent two possible ways to release spin frustration (spin-driven Jahn–Teller distortion). Our paradigm provides a simple, yet rigorous, route to uncover the electronic structure of PNTM clusters and may be applied to a wide variety of such clusters.

A theoretical study of adsorption on iron sulfides towards nanoparticle modeling

Surface modification of zero-valent iron (nZVI) nanoparticles, which are frequently used in the removal of chlorinated hydrocarbons from contaminated groundwater, can increase their surface stability without significant loss of reactivity. Sulfidation is a process during which thin iron sulfide phases are formed on nZVI particles. In this work, the adsorption capability of two iron sulfide minerals (mackinawite and pyrite) and ZVI with respect to two small polar molecules (H2O and H2S) and trichloroethylene (TCE) was modeled by using the quantum mechanics (QM) approach. High-level QM methods used on cluster models helped in benchmarking and validation of density functional theory methods used on periodic slab models of the (001) surfaces of iron sulfides and the (111) surface of ZVI. This careful computational treatment was necessary for achieving reliable results because modeled iron containing compounds represent computationally demanding systems. The results showed that adsorption was strongly affected by surface topology, accessibility of surface sites, and the shape of adsorbed molecular species. The mackinawite surface is practically hydrophobic having weak interactions with polar molecules (about -5/-6 kcal mol-1), in contrast to the surfaces of pyrite and ZVI (adsorption energies are about three times larger). On the other hand, the adsorption of weakly polar planar TCE molecule is relatively strong and similar for all three surfaces (in the range of -11 to -17 kcal mol-1). Moreover, it was shown that the dominant component of the adsorption energy of TCE had originated from dispersion interactions, which were less important for small polar molecules.

Structural and Electronic Rearrangements in Fe2S2, Fe3S4, and Fe4S4 Atomic Clusters under the Attack of NO, CO, and O2

We report results, based on density functional theory-generalized gradient approximation calculations, that shed light on how NO, CO, and O₂ interact with Fe₂S₂, Fe₃S₄, and Fe₄S₄ clusters and how they modify their structural and electronic properties. The interest in these small iron sulfide clusters comes from the fact that they are at the protein cores and that elucidating fundamental aspects of their interaction with those light molecules which are known to modify their functionality may help in understanding complex behaviors in biological systems. CO and NO are found to bind molecularly, leading to moderate relaxations in the clusters, but nevertheless to changes in the spin-polarized electronic structure and related properties. In contrast, dissociative chemisorption of O₂ is much more stable than molecular adsorption, giving rise to significant structural distortions, particularly in Fe₄S₄ that splits into two Fe₂S₂ subclusters. As a consequence, oxygen tends to strongly reduce the spin polarization in Fe and to weaken the Fe-Fe interaction inducing antiparallel couplings that, in the case of Fe₄S₄, clearly arise from indirect Fe-Fe exchange coupling mediated by O. The three molecules (particularly CO) enhance the stability of the iron-sulfur clusters. This increase is noticeably more pronounced for Fe₂S₂ than for the other iron-sulfur clusters of different compositions, a result that correlates with the fact that in recent experiments of CO reaction with Fe_mS_m (m = 1-4), the Fe₂S₂CO product results as a prominent one.

Fe-V sulfur clusters studied through photoelectron spectroscopy and density functional theory

Iron-vanadium sulfur cluster anions are studied by photoelectron spectroscopy (PES) at 3.492 eV (355 nm) and 4.661 eV (266 nm) photon energies, and by density functional theory (DFT) calculations. The structural properties, relative energies of different structural isomers, and the calculated first vertical detachment energies (VDEs) of different structural isomers for cluster anions FeVS1-3- and FemVnSm+n- (m + n = 3, 4; m > 0, n > 0) are investigated at a BPW91/TZVP theory level. The experimental first VDEs for these Fe-V sulfur clusters are reported. The most probable ground state structures and spin multiplicities for these clusters are tentatively assigned by comparing their theoretical and experiment first VDE values. For FeVS1-3- clusters, their first VDEs are generally observed to increase with the number of sulfur atoms from 1.45 eV to 2.86 eV. The NBO/HOMOs of the ground state of FeVS1-3- clusters are localized in a p orbital on a S atom; the partial charge distribution on the NBO/HOMO localized site of each cluster anion is responsible for the trend of their first VDEs. A less negative localized charge distribution is correlated with a higher first VDE. Structure and steric effect differences for FemVnSm+n- (m + n = 3, m > 0, n > 0) clusters are suggested to be responsible for their different first VDEs and properties. Two types of structural isomers are identified for FemVnSm+n- (m + n = 4, m > 0, n > 0) clusters: a tower structure isomer and a cubic structure isomer. The first VDEs for tower like isomers are generally higher than those for cubic like isomers of FemVnSm+n- (m + n = 4, m > 0, n > 0) clusters. Their first VDEs are can be understood through: (1) NBO/HOMO distributions, (2) structures (steric effects), and (3) partial charge numbers on the NBO/HOMO's localized sites. EBEs for excited state transitions for all Fe-V sulfur clusters are calculated employing OVGF and TDDFT approaches at the TZVP level. The OVGF approach for these Fe/V/S cluster anions is better for the higher transition energies than the TDDTF approach. The experimental and theoretical results for these Fe/V/S cluster anions are compared with their related pure iron sulfur cluster anions. Properties of the NBO/HOMO are essential for understanding and estimating the different first VDEs for Fe/V/S, and comparing them to those of the pure Fe/S cluster anions.

Thermal stability of iron-sulfur clusters

The thermal decomposition of free cationic iron-sulfur clusters Fe_xS_y⁺ (x = 0-7, y = 0-9) is investigated by collisional post-heating in the temperature range between 300 and 1000 K. With increasing temperature the preferential formation of stoichiometric Fe_xS_y⁺ (y = x) or near stoichiometric Fe_xS_y⁺ (y = x ± 1) clusters is observed. In particular, Fe₄S₄⁺ represents the most abundant product up to 600 K, Fe₃S₃⁺ and Fe₃S₂⁺ are preferably formed between 600 K and 800 K, and Fe₂S₂⁺ clearly dominates the cluster distribution above 800 K. These temperature dependent fragment distributions suggest a sequential fragmentation mechanism, which involves the loss of sulfur and iron atoms as well as FeS units, and indicate the particular stability of Fe₂S₂⁺. The potential fragmentation pathways are discussed based on first principles calculations and a mechanism involving the isomerization of the cluster prior to fragmentation is proposed. The fragmentation behavior of the iron-sulfur clusters is in marked contrast to the previously reported thermal dissociation of analogous iron-oxide clusters, which resulted in the release of O₂ molecules only, without loss of metal atoms and without any tendency to form particular prominent and stable Fe_xO_y⁺ clusters at high temperatures.

Electronic, magnetic structure and water splitting reactivity of the iron-sulfur dimers and their hexacarbonyl complexes: A density functional study

The iron sulfide dimers (FeS)2 and their persulfide isomers with S-S bonds are studied with the B3LYP density functional as bare clusters and as hexacarbonyls. The disulfides are more stable than the persulfides as bare clusters and the persulfide ground state lies at 3.2 eV above the global minimum, while in the hexacarbonyl complexes this order is reversed: persulfides are more stable, but the energy gap between disulfides and persulfides becomes much smaller and the activation barrier for the transition persulfide → disulfide is 1.11 eV. Carbonylation also favors a non-planar Fe2S2 ring for both the disulfides and the persulfides and high electron density in the Fe2S2 core is induced. The diamagnetic ordering is preferred in the hexacarbonyls, unlike the bare clusters. The hexacarbonyls possess low-lying triplet excited states. In the persulfide, the lowest singlet-to-triplet state excitation occurs by electron transition from the iron centers to an orbital located predominantly at S2 via metal-to-ligand charge transfer. In the disulfide this excitation corresponds to ligand-to-metal charge transfer from the sulfur atoms to an orbital located at the iron centers and the Fe-Fe bond. Water splitting occurs on the hexacarbonyls, but not on the bare clusters. The singlet and triplet state reaction paths were examined and activation barriers were determined: 50 kJ mol(-1) for HO-H bond dissociation and 210 kJ mol(-1) for hydrogen evolution from the intermediate sulfoxyl-hydroxyl complexes Fe2S(OH)(SH)(CO)6 formed. The lowest singlet-singlet excitations in the hexacarbonyls, the water adsorption complexes and in the reaction intermediates, formed prior to dihydrogen release, fall in the visible light region. The energy barrier of 210 kJ mol(-1) for the release of one hydrogen molecule corresponds to one visible photon of 570 nm. The dissociation of a second water molecule, followed by H2 and O2 release via hydro-peroxide intermediate is a two-step process, with activation barriers of 218 and 233 kJ mol(-1), which also fall in the visible light region. A comparison of the full reaction path with that on diiron dioxide hexacarbonyls Fe2O2(CO)6 is traced.

Aqueous Fe2S2 cluster: structure, magnetic coupling, and hydration behaviour from Hubbard U density functional theory

We present a DFT + U investigation of the all-ferrous Fe2S2 cluster in aqueous solution. We determine the value of U by tuning the geometry of the cluster in the gas-phase to that obtained by the highly accurate CCSD(T) method. When the optimised value of U is employed for the aqueous Fe2S2 cluster (Fe2S2(aq)), the resulting geometry agrees well with the X-ray diffraction structure, while the magnetic coupling is in line with the estimate from Mössbauer data. Molecular dynamics trajectories predict Fe2S2(aq) to be stable in water, regardless of the introduction of U. However, significant differences arise in the geometry, hydration, and exchange constant of the solvated clusters.

Anatomy of an iron-sulfur cluster scaffold protein: Understanding the determinants of [2Fe-2S] cluster stability on IscU

Protein-bound iron sulfur clusters are prosthetic groups involved in several metabolic pathways. Understanding how they interact with the host protein and which factors influence their stability is therefore an important goal in biology. Here, we have addressed this question by studying the determinants of the 2Fe-2S cluster stability in the IscU/Isu protein scaffold. Through a detailed computational study based on a mixed quantum and classical mechanics approach, we predict that the simultaneous presence of two conserved residues, D39 and H105, has a conflicting role in cluster coordination which results in destabilizing cluster-loaded IscU/Isu according to a 'tug-of-war' mechanism. The effect is absent in the D39A mutant already known to host the cluster more stably. Our theoretical conclusions are directly supported by experimental data, also obtained from the H105A mutant, which has properties intermediate between the wild-type and the D39A mutant. This article is part of a Special Issue entitled: Fe/S proteins: Analysis, structure, function, biogenesis and diseases.

Analysis of differences in oxygen sensitivity of Fe-S clusters

Many but not all iron-sulphur clusters in metalloproteins are known to be sensitive to molecular oxygen with dramatic consequences for their biological function. We performed a systematic quantum chemical investigation that sheds light on the differences in oxygen sensitivity depending on charge and spin states of these clusters as well as on their spatial fixation by the enzyme's scaffold. We find that significant structural distortions are required to bind O2 exothermically to [Fe2S2] and [Fe3S4] clusters, while only small conformational changes allow for the thermodynamically favorable coordination of molecular oxygen to [Fe4S4] cubanes and [Fe4S3] clusters.

Experimental and theoretical studies of ammonia generation: Reactions of H2 with neutral cobalt nitride clusters

Ammonia generation through reaction of H(2) with neutral cobalt nitride clusters in a fast flow reactor is investigated both experimentally and theoretically. Single photon ionization at 193 nm is used to detect neutral cluster distributions through time-of-flight mass spectrometry. Co(m)N(n) clusters are generated through laser ablation of Co foil into N(2)/He expansion gas. Mass peaks Co(m)NH(2) (m = 6, 10) and Co(m)NH(3) (m = 7, 8, 9) are observed for reactions of H(2) with the Co(m)N(n) clusters. Observation of these products indicates that clusters Co(m)N (m = 7, 8, 9) have high reactivity with H(2) for ammonia generation. Density functional theory (DFT) calculations are performed to explore the potential energy surface for the reaction Co(7)N + 3∕2H(2) → Co(7)NH(3), and a barrierless, thermodynamically favorable pathway is obtained. An odd number of hydrogen atoms in Co(m)NH(3) (m = 7, 8, 9) probably come from the hydrogen molecule dissociation on two active cobalt nitride clusters based on the DFT calculations. Both experimental observations and theoretical calculations suggest that hydrogen dissociation on two active cobalt nitride clusters is the key step to form NH(3) in a gas phase reaction. A catalytic cycle for ammonia generation from N(2) and H(2) on a cobalt metal catalyst surface is proposed based on our experimental and theoretical investigations.

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.

Electronic structures and chemical bonding in diatomic ScX to ZnX (X = S, Se, Te)

Bond distances, vibrational frequencies, electron affinities, ionization potentials, dissociation energies, and dipole moments of the title molecules in neutral, positively, and negatively charged ions were studied using density functional method. Ground electronic state was assigned for each molecule. The bonding patterns were analyzed and compared with both the available data and across the series. It was found that, besides ionic component, covalent bonds are formed between the metal s, d orbitals, and the p orbital of S, Se, and Te. For neutral and cationic molecules, the covalent character increases from ScX to CrX and from FeX to CuX with an exception of decrease at MnX and ZnX, while for anionic molecules, the trend is not obvious. For both neutral and charged molecules, the sulfides have the shortest bond distance and largest vibrational frequency, while tellurides have the largest bond distance and smallest vibrational frequency. For neutral and anionic molecules, the dissociation energy of sulfides is the largest, that of tellurides is the smallest, while this only remains true for cationic molecules from ScX(+) to FeX(+).

The Ni2 + O2 reaction: the IR spectrum and structure of Ni2O2. A combined IR matrix isolation and theoretical study

The formation of Ni2O2 can be observed from the condensation of effusive beams of Ni and O2 in neon or argon matrices. Observation of 58Ni(2)16O2, 58Ni60Ni16O2, 60Ni2(16)O2, Ni(2)18O2 and Ni(2)16O18O isotopic data for five fundamental transitions enable a discussion of structural parameters for matrix-isolated Ni2O2 in its cyclic ground state. Analysis of the nickel isotopic effects on the 58,60Ni2(16)O18O fundamentals suggest an elongated rhombic structure with a Ni-O bond force constant (240+/-10 N m-1) and NiONi bond angles around 79 degrees. The latter points to a Ni-Ni internuclear distance shorter than the O-O one. Low-lying singlet, triplet and quintet states have been studied using density functional theory with an unrestricted wave function and broken symmetry formalism. The high spin states and closed shell singlet states have been also investigated at the CCSD(T) level. The Ni2O2 ground state is calculated to be an antiferromagnetic singlet state with all the hybrid functionals. The first order properties (energies, geometry) calculated with a hybrid functional are very similar when different exchange-correlation functionals with different exact exchange fractions are used and the calculated ground state geometry (NiONi bond angle near 80 degrees, NiO bond distance around 179.5 pm) is in good agreement with the experimental estimate. Nevertheless, a correct reproduction of the experimental vibrational properties is found only when a hybrid functional containing an exact exchange fraction in the 0.4-0.5 range is used. The orbital and topological bonding analyses of Ni2O2 reveal that the relatively short Ni-Ni internuclear distance within the molecule should not be interpreted as a remaining metal-metal bonding interaction, but clearly indicate that the bonding driving force is due to the formation of four strong and highly polarized Ni-O bonds. Even in such an early stage of metal oxidation, the Ni-Ni interaction has virtually disappeared.

Gas phase infrared spectroscopy of mono- and divanadium oxide cluster cations

The vibrational spectroscopy of the mono- and divanadium oxide cluster cations VO(1-3)+ and V2O(2-6)+ is studied in the region from 600 to 1600 wave numbers by infrared photodissociation of the corresponding cluster cation-helium atom complexes. The comparison of the experimental depletion spectra with the results of density functional calculations on bare vanadium oxide cluster cations allows for an unambiguous identification of the cluster geometry in most cases and, for VO(1-3)+ and V2O(5,6)+, also of the electronic ground state. A common structural motif of all the studied divanadium cluster cations is a four-membered V-O-V-O ring, with three characteristic absorption bands in the 550-900 wave number region. For the V-O-V and V=O stretch modes the relationship between vibrational frequencies and V-O bond distances follows the Badger rule.

Electronic ground states of the V2O4+/0/− species from multireference correlation and density functional studies

The molecular and electronic structures of the V2O4+/0/- species are examined by multireference averaged coupled-pair functional (MR-ACPF) and density functional B3LYP calculations. For all three species, new conformers have been found. Shallow potential energy curves imply high mobility of the oxygen atoms in the neutral and anionic species for which antiferromagnetic coupling of the weakly interacting 3dV electrons is found. Good agreement between the MR-ACPF and B3LYP results for the molecular structures and the relative energies of states with different spin multiplicity, as well as for the ionization energy and electron affinity, is observed. For the computation of the height of the transition barriers between different conformers elaborated MR-ACPF calculations are required.

Electronic States of Fe2S-/0/+

The relative energies of a multitude of low-lying electronic states of Fe2S-/0/+ are determined by complete active space self-consistent field (CASSCF) calculations. The numerous states obtained are assigned to spin ladders. For selected states, dynamic correlation has been included by multireference configuration interaction (MRCI) and the structures of some high-spin states have been optimized by CASSCF/MRCI. Comparison is made with structures obtained by density-functional theoretical calculations. The ground states of Fe2S-/0/+ are 10B2, 1A1 and 8A2, respectively, and the total splittings of the lowest-energy spin ladders are about 0.18, 0.07 and 0.13 eV, respectively. The spin ladders of Fe2S qualitatively reflect the picture of Heisenberg spin coupling. While both Fe2S- and Fe2S+ show an Fe-Fe distance of about 270 pm, that of Fe2S is about 100 pm longer. The calculated adiabatic electron affinity of Fe2S is 1.2 eV and the ionization energy 6.6 eV. An interpretation of the observed photoelectron spectrum of Fe2S- is given.