Scanning the potential energy surface of iron clusters: A novel search strategy

Structural Determination and Hierarchical Evolution of Transition Metal Clusters Based on an Improved Self-Adaptive Differential Evolution with Neighborhood Search Algorithm

Determining the optimal structures and clarifying the corresponding hierarchical evolution of transition metal clusters are of fundamental importance for their applications. The global optimization of clusters containing a large number of atoms, however, is a vastly challenging task encountered in many fields of physics and chemistry. In this work, a high-efficiency self-adaptive differential evolution with neighborhood search (SaNSDE) algorithm, which introduced an optimized cross-operation and an improved Basin Hopping module, was employed to search the lowest-energy structures of CoN, PtN, and FeN (N = 3-200) clusters. The performance of the SaNSDE algorithm was first evaluated by comparing our results with the parallel results collected in the Cambridge Cluster Database (CCD). Subsequently, different analytical methods were introduced to investigate the structural and energetic properties of these clusters systematically, and special attention was paid to elucidating the structural evolution with cluster size by exploring their overall shape, atomic arrangement, structural similarity, and growth pattern. By comparison with those results listed in the CCD, 13 lower-energy structures of FeN clusters were discovered. Moreover, our results reveal that the clusters of three metals had different magic numbers with superior stable structures, most of which possessed high symmetry. The structural evolution of Co, Pt, and Fe clusters could be, respectively, considered as predominantly closed-shell icosahedral, Marks decahedral, and disordered icosahedral-ring growth. Further, the formation of shell structures was discovered, and the clusters with hcp-, fcc-, and bcc-like configurations were ascertained. Nevertheless, the growth of the clusters was not simply atom-to-atom piling up on a given cluster despite gradual saturation of the coordination number toward its bulk limit. Our work identifies the general growth trends for such a wide region of cluster sizes, which would be unbearably expensive in first-principles calculations, and advances the development of global optimization algorithms for the structural prediction of clusters.

Halogen Doping to Control the Band Gap of Ascorbic Acid: A Theoretical Study

Ascorbic acid is an important antioxidant agent that acts as an electron donor and is involved in many physiological processes. Structural modification in ascorbic acid is a subject of extensive biochemical research due to its involvement in a variety of relevant phenomena including electron transport, complex redox reactions, neurochemical reactions, enzymatic reactions, and chemotherapeutic potential. In this work, the structure of ascorbic acid is modified via doping with the first three members of the halogen group to investigate the changes in the electronic structure and spectroscopic parameters using first-principles methods. To obtain the lowest-energy structures, different basis sets in density functional theory (DFT) and Hartree-Fock approaches were employed in the geometry optimization process. The potential energy maps of the structures were computed to study the molecular orientations and their optical and electrical properties. The spectroscopic properties were computed via UV-vis and nuclear magnetic resonance (NMR) spectroscopies to study the effects of doping into the compound. To obtain further insights into the chemical structure, the Fourier transform infrared (FT-IR) spectra of the materials were theoretically investigated. It was found that the band gap is sensitive to doping as we moved from fluorine to chlorine and then to bromine.

Kinetics of stepwise nitrogen adsorption by size-selected iron cluster cations: Evidence for size-dependent nitrogen phobia

We present a study of stepwise cryogenic N₂ adsorption on size-selected Fe_n ⁺ (n = 8-20) clusters within a hexapole collision cell held at T = 21-28 K. The stoichiometries of the observed adsorption limits and the kinetic fits of stepwise N₂ uptake reveal cluster size-dependent variations that characterize four structural regions. Exploratory density functional theory studies support tentative structural assignment in terms of icosahedral, hexagonal antiprismatic, and closely packed structural motifs. There are three particularly noteworthy cases, Fe₁₃ ⁺ with a peculiar metastable adsorption limit, Fe₁₇ ⁺ with unprecedented nitrogen phobia (inefficient N₂ adsorption), and Fe₁₈ ⁺ with an isomeric mixture that undergoes relaxation upon considerable N₂ uptake.

Evolution of Ferromagnetic and Antiferromagnetic States in Iron Nitride Clusters FenN and FenN2 (n = 1-10)

First-principles density functional theory calculations on neutral and singly negatively and positively charged iron clusters Fe_n and iron nitride clusters Fe_nN and Fe_nN₂ (n = 1-10) in the range of 1 ≤ n ≤ 10 revealed that there is a strong competition between ferromagnetic and antiferromagnetic states especially in the Fe_nN₂^0,±1 cluster series. This phenomenon was related to superexchange via a bridging N atom between two iron atoms in the Fe_nN₂^0,±1 cluster series and to a double superexchange effect via a Fe atom shared by two N atoms in the Fe_nN₂^0,±1 series. A thorough examination of the structure-energy-spin state relationships in these clusters is conducted, leading to new insights and confirmation of available experimental results on structural parameters and dissociation energetics. The bond energies of both nitrogen atoms in the Fe_nN₂ series are approximately the same. They weakly depend on the charge of the host cluster and fluctuate around 5.5 eV when moving along the series. The energy of N₂ desorption is relatively small; it varies by about 1.0 eV and depends on the charge of the cluster. The experimental finding that N₂ dissociates on the Fe_n⁺ clusters beginning with n = 4 was supported by the results of our computations. Our computed values of the Fe_n⁺-N bonding energies agree with the experimental data within the experimental uncertainty bars. It was found that the attachment of one or two N atoms does not seriously affect the polarizability, electron affinity, or ionization energy of the host iron clusters independent of the charge.

Dissociation of dinitrogen on iron clusters: a detailed study of the Fe16 + N2 case

The coalescence of two Fe8N as well as the structure of the Fe16N2 cluster were studied using density functional theory with the generalized gradient approximation and a basis set of triple-zeta quality. It was found that the coalescence may proceed without an energy barrier and that the geometrical structures of the resulting clusters depend strongly on the mutual orientations of the initial moieties. The dissociation of N2 is energetically favorable on Fe16, and the nitrogen atoms share the same Fe atom in the lowest energy state of the Fe16N2 species. The attachment of two nitrogen atoms leads to a decrease in the total spin magnetic moment of the ground-state Fe16 host by 6 μB due to the peculiarities of chemical bonding in the magnetic clusters. In order to gain insight into the dependence of properties on charge and to estimate the bonding energies of both N atoms, we performed optimizations of Fe16N and the singly charged ions of both Fe16N2 and Fe16N. It was found that the electronic properties of the Fe16N2 cluster, such as electron affinity and ionization energy, do not appreciably depend on the attachment of nitrogen atoms but that the average binding energy per atom changes significantly. The lowering in total energy due to the attachment of two N atoms was found to be nearly independent of charge. The IR and Raman spectra were simulated for Fe16N2 and its ions, and it was found that the positions of the most intense peaks in the IR spectra strongly depend on charge and therefore present fingerprints of the charged states. The chemical bonding in the ground-state Fe16N20,±1 species was described in terms of the localized molecular orbitals.

Density-functional tight-binding: basic concepts and applications to molecules and clusters

The scope of this article is to present an overview of the Density Functional based Tight Binding (DFTB) method and its applications. The paper introduces the basics of DFTB and its standard formulation up to second order. It also addresses methodological developments such as third order expansion, inclusion of non-covalent interactions, schemes to solve the self-interaction error, implementation of long-range short-range separation, treatment of excited states via the time-dependent DFTB scheme, inclusion of DFTB in hybrid high-level/low level schemes (DFT/DFTB or DFTB/MM), fragment decomposition of large systems, large scale potential energy landscape exploration with molecular dynamics in ground or excited states, non-adiabatic dynamics. A number of applications are reviewed, focusing on -(i)- the variety of systems that have been studied such as small molecules, large molecules and biomolecules, bare orfunctionalized clusters, supported or embedded systems, and -(ii)- properties and processes, such as vibrational spectroscopy, collisions, fragmentation, thermodynamics or non-adiabatic dynamics. Finally outlines and perspectives are given.

Exploring the potential energy surface of small lead clusters using the gradient embedded genetic algorithm and an adequate treatment of relativistic effects

Theoretical inclusion of relativistic effects (scalar and spin–orbit) play a crucial role to assure an adequate structural assignment on lead clusters.

The spin and orbital contributions to the total magnetic moments of free Fe, Co, and Ni clusters

We present size dependent spin and orbital magnetic moments of cobalt (Con (+), 8 ≤ n ≤ 22), iron (Fen (+), 7 ≤ n ≤ 17), and nickel cluster (Nin (+), 7 ≤ n ≤ 17) cations as obtained by X-ray magnetic circular dichroism (XMCD) spectroscopy of isolated clusters in the gas phase. The spin and orbital magnetic moments range between the corresponding atomic and bulk values in all three cases. We compare our findings to previous XMCD data, Stern-Gerlach data, and computational results. We discuss the application of scaling laws to the size dependent evolution of the spin and orbital magnetic moments per atom in the clusters. We find a spin scaling law "per cluster diameter," ∼n(-1/3), that interpolates between known atomic and bulk values. In remarkable contrast, the orbital moments do likewise only if the atomic asymptote is exempt. A concept of "primary" and "secondary" (induced) orbital moments is invoked for interpretation.

Theoretical study of neutral and charged Fe7-(C6H6)m, m = 1, 2 rice-ball clusters

Bonding of benzene molecules on the surface of neutral and charged Fe7 clusters, which have pentagonal bipyramids (PBP), was studied by means of all-electrons density functional calculations. Dispersion corrections were done with the BPW91-D2 method using the 6-311++G(2d,2p) basis sets. With two less coordinated equatorial sites (bonded to four iron atoms) and one axial site (bonded to five atoms), a triangular face of Fe7 emerges as the basic unit for the absorption of benzene moieties. Bonding of benzene (Bz) on such triangle yields the ground state (GS) for Fe7Bz, Fe7Bz(-), and Fe7Bz(+). Without dispersion, in the GS of Fe7Bz(-), the ligand is η(6) coordinated with a single equatorial iron site, and in the GSs of Fe7Bz2 and Fe7Bz2(-), each benzene moiety is η(6) bonded on opposite equatorial sites. However, BPW91-D2 yields GS structures for Fe7Bz2, Fe7Bz2(-), and Fe7Bz2(+), where the absorption is done on opposite triangles. Therefore, dispersion corrections are crucial for a proper study of Fe7Bz2. The multiplicities (M = 2S + 1, where S is the total spin) of these species, 17, 16, and 18, respectively, are smaller than those of Fe7(23), Fe7(-)(22) and Fe7(+)(24) showing important quenching of the magnetic moment of Fe7. Bond dissociation energies (BDE), in kcal/mol, for Fe7Bz (32.7), Fe7Bz(+) (47.3), and Fe7Bz(-) (27.2) show bigger (smaller) values for the cation (anion). A similar picture was found for the BDEs of Fe7Bz2. Ionization energies, 5.37 and 4.94 eV, for m = 1 and 2 are smaller than that of Fe7, 6.00 eV; which is due to delocalization of the electrons through the network of 3d-π bonds. Electron affinities of Fe7Bz1,2 are also smaller than that of Fe7, being mainly due to the increased repulsion.

Antiferromagnetic-like coupling in the cationic iron cluster of thirteen atoms

We explore, within the density functional theory in the generalized gradient approximation to exchange and correlation, the map of spin isomers of the cationic Fe13(+) cluster in connection with recent X-ray magnetic circular dichroism spectroscopy experiments [M. Niemeyer et al., Phys. Rev. Lett. 2012, 108, 057201] which showed an anomalous low magnetic moment per number of 3d holes in this cluster. We systematically explore the low-lying magnetic excitations and correlate them with structural rearrangements and stability indicators. We obtain the observed low magnetic moment per 3d hole as the ground state of Fe13(+) and we demonstrate that, as supposed by the experimentalists, the cluster undergoes a magnetic transition from a ferromagnetic-like configuration to an antiferromagnetic-like one upon ionization. We unravel this unexpected magnetic behavior showing that it is concomitant with a Th-deformation of the icosahedral structure together with the electronic filling of this particular iron cluster. The spin-orbit interaction preserves this magnetic configuration which is essentially due to the spin. Our computed magnetic anisotropy energy supports the experimental interpretation of the cluster as fluxional due to the very weak coupling of the magnetic moment to an easy axis.

Spin coupling and orbital angular momentum quenching in free iron clusters

Magnetic spin and orbital moments of size-selected free iron cluster ions Fe{n}{+} (n=3-20) have been determined via x-ray magnetic circular dichroism spectroscopy. Iron atoms within the clusters exhibit ferromagnetic coupling except for Fe{13}{+}, where the central atom is coupled antiferromagnetically to the atoms in the surrounding shell. Even in very small clusters, the orbital magnetic moment is strongly quenched and reduced to 5%-25% of its atomic value while the spin magnetic moment remains at 60%-90%. This demonstrates that the formation of bonds quenches orbital angular momenta in homonuclear iron clusters already for coordination numbers much smaller than those of the bulk.

Bonding and magnetism of Fe(6)-(C(6)H(6))(m), m = 1, 2

The interactions of one and two benzene molecules with the superparamagnetic Fe(6) cluster were studied by means of gradient-corrected density functional theory. The ground state, GS, of bare Fe(6) presents a distorted octahedral structure with 2S = 20; S is the total spin. For the calculated 2S = 16 GS of the neutral Fe(6)-C(6)H(6) complex, as well as in the positive and negative ions both with 2S = 15, the benzene unit is adsorbed on one axial Fe(a) atom. The 2S = 14 GS for Fe(6)-(C(6)H(6))(2) resembles a sandwich structure, with the metal Fe(6) cluster separating the benzene rings that are bonded symmetrically on the two axial sites of Fe(6). The binding is accounted for by electrostatic interactions and by 3d-pi bonds, as revealed by the molecular orbitals. Though each C-Fe bond is weak, eta(6) coordinations were indicated by the topology of the electronic density. The 3d-pi bonding is reflected by the adiabatic ionization energies and electron affinities, which are smaller than those of bare Fe(6). The computed IR spectra show vibrational bands near those of bare benzene; some forbidden IR modes in benzene and in Fe(6) become IR active in Fe(6)-(C(6)H(6))(1,2). The results show a strong perturbation of the electronic structure of Fe(6). The decrease of its magnetic moment implies that the magnetic effects play an important role in the adsorption of benzene.

Assessment of density functional theory optimized basis sets for gradient corrected functionals to transition metal systems: The case of small Nin (n⩽5) clusters

Density functional calculations have been performed for small nickel clusters, Ni(n), Ni(n) (+), and Ni(n)(-) (n<or=5), using the linear combination of Gaussian-type orbital density functional theory approach. Newly developed nickel all-electron basis sets optimized for generalized gradient approximation (GGA) as well as an all-electron basis set optimized for the local density approximation were employed. For both neutral and charged systems, several isomers and different multiplicities were studied in order to determine the lowest energy structures. A vibrational analysis was performed in order to characterize these isomers. Structural parameters, harmonic frequencies, binding energies, ionization potentials, and electron affinities are reported. This work shows that the employed GGA basis sets for the nickel atom are important for the correct prediction of the ground state structures of small nickel clusters and that the structural assignment of these systems can be performed, with a good resolution, over the ionization potential.

Global minimum structure searches via particle swarm optimization

Novel implementation of the evolutionary approach known as particle swarm optimization (PSO) capable of finding the global minimum of the potential energy surface of atomic assemblies is reported. This is the first time the PSO technique has been used to perform global optimization of minimum structure search for chemical systems. Significant improvements have been introduced to the original PSO algorithm to increase its efficiency and reliability and adapt it to chemical systems. The developed software has successfully found the lowest-energy structures of the LJ(26) Lennard-Jones cluster, anionic silicon hydride Si(2)H(5) (-), and triply hydrated hydroxide ion OH(-) (H(2)O)(3). It requires relatively small population sizes and demonstrates fast convergence. Efficiency of PSO has been compared with simulated annealing, and the gradient embedded genetic algorithm.

Structure of the Na(x)Cl(x+1) (-) (x=1-4) clusters via ab initio genetic algorithm and photoelectron spectroscopy

The application of the ab initio genetic algorithm with an embedded gradient has been carried out for the elucidation of global minimum structures of a series of anionic sodium chloride clusters, Na(x)Cl(x+1) (-) (x=1-4), produced in the gas phase using electrospray ionization and studied by photoelectron spectroscopy. These are all superhalogen species with extremely high electron binding energies. The vertical electron detachment energies for Na(x)Cl(x+1) (-) were measured to be 5.6, 6.46, 6.3, and 7.0 eV, for x=1-4, respectively. Our ab initio gradient embedded genetic algorithm program detected the linear global minima for NaCl(2) (-) and Na(2)Cl(3) (-) and three-dimensional structures for the larger species. Na(3)Cl(4) (-) was found to have C(3v) symmetry, which can be viewed as a Na(4)Cl(4) cube missing a corner Na(+) cation, whereas Na(4)Cl(5) (-) was found to have C(4v) symmetry, close to a 3x3 planar structure. Excellent agreement between the theoretically calculated and the experimental spectra was observed, confirming the obtained structures and demonstrating the power of the developed genetic algorithm technique.

Activation of Methane by the Iron Dimer Cation. A Theoretical Study

A detailed investigation of the reaction mechanisms underlying the observed reactivity of the iron dimer cation with respect to methane has been performed by density functional hybrid (B3LYP) and nonhybrid (BPW91) calculations. Minima and transition states have been fully optimized and characterized along the potential energy surfaces leading to three different exit channels for both the ground and the first excited states of the dimer. A comparison with our previous work covering the reactivity of the Fe(+) monomer was made to underline similarities and differences of the reaction mechanisms. Results show that geometric arrangements corresponding to bridged positions of the ligands with respect to iron atoms are always favored and stabilize intermediates, transition states and products, facilitating their formation. Binding energies of reaction products have been computed and compared with experimental measurements, and ELF analysis of the bond has been performed to rationalize trends as a function of the structure.

Mindless Chemistry

Applications of an automated stochastic search procedure for locating all possible minima with a given composition are illustrated by the pentatomic molecules BCNOS, CAlSiPS, C(4)B(-), C(4)Al(-), and CBe(4)(2-), as well as by C(6)Be, the C(6)Be(2-) dianion, and C(6)H(2). All previously identified minima were reproduced, and many new structures, often with nonintuitive geometries, were found.

Structure and shape variations in intermediate-size copper clusters

Using extensive, unbiased searches based on density-functional theory, we explore the structural evolution of Cu(n) clusters over the size range n=8-20. For n=8-16, the optimal structures are plateletlike, consisting of two layers, with the atoms in each layer forming a trigonal bonding network similar to that found in smaller, planar clusters (n<or=6). For n=17 and beyond, there is a transition to compact structures containing an icosahedral 13-atom core. The calculated ground-state structures are significantly different from those predicted earlier in studies based on empirical and semiempirical potentials. The evolution of the structure and shape of the preferred configuration of Cu(n), n<or=20, is shown to be nearly identical to that found for Na clusters, indicating a shell-model-type behavior in this size range.

Structure, bonding, and magnetism in manganese clusters

We investigate the structures and magnetic properties of small Mn(n) clusters in the size range of 2-13 atoms using first-principles density functional theory. We arrive at the lowest energy structures for clusters in this size range by simultaneously optimizing the cluster geometries, total spins, and relative orientations of individual atomic moments. The results for the net magnetic moments for the optimal clusters are in good agreement with experiment. The magnetic behavior of Mn(n) clusters in the size range studied in this work ranges from ferromagnetic ordering (large net cluster moment) for the smallest (n=2, 3, and 4) clusters to a near degeneracy between ferromagnetic and antiferromagnetic solutions in the vicinity of n=5 and 6 to a clear preference for antiferromagnetic (small net cluster moment) ordering at n=7 and beyond. We study the details of this evolution and present a picture in which bonding in these clusters predominantly occurs due to a transfer of electrons from antibonding 4s levels to minority 3d levels.

Reactions of cationic iron clusters with ammonia, models of nitrogen hydrogenation and dehydrogenation

The gas phase reactivities of small cationic iron clusters, Fen+ (n = 1-20), towards ammonia were investigated using Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry. Sequential addition of ammonia molecules to the clusters was observed to be the dominating process for n > 4. In the case of n = 4 we observed addition of ammonia accompanied by dehydrogenation. This reaction was modelled using hybrid density functional theory. Clusters with n < 4 do not react with ammonia. Clusters Fen+ (n = 1-20) react with neither N2 nor H2 at around 10(-8) mbar. When dinitrogen was seeded into the expanding helium, mixed clusters of the type FenNm+ were observed. These ions react with H2, either by addition, or by substitution of N2. The clusters with m = 1 were isolated in separate experiments and reacted with H2, which showed that mixed clusters with n = 5-13 add up to 5 molecules of dihydrogen in successive slow reactions.

Degradation of inter-atomic bonds during structural phase change in intermediate Ni-clusters (Ni39–Ni49)

Results based on a symmetry- and spin-unrestricted tight-binding molecular-dynamics study are presented for the ground-state geometries of intermediate Ni(n), n in [39,49], clusters. A structural phase change is found to take place around n=43 during which a structural transition from fcc/hcp structure to icosahedral one is observed. This is in good agreement with recent experimental findings. This structural transition is found to be associated with a degradation of the inter-atomic bond energy which indicates that the inter-atomic bond does not only depend on the coordination number of each atom but also on its point group symmetry.