Stern-Gerlach experiments of one-dimensional metal-benzene sandwich clusters: Mn(C6H6)m (M = Al, Sc, Ti, and V)

A molecular beam of multilayer metal-benzene organometallic clusters Mn(C6H6)m (M = Al, Sc, Ti, and V) was produced by a laser vaporization synthesis method, and their magnetic deflections were measured. Multidecker sandwich clusters of transition-metal atoms and benzene Scn(C6H6)n+1 (n = 1, 2) and Vn(C6H6)n+1 (n = 1-4) possess magnetic moments that increase monotonously with n. The magnetic moments of Al(C6H6), Scn(C6H6)n+1, and Vn(C6H6)n+1 are smaller than that of their spin-only values as a result of intracluster spin relaxation, an effect that depends on the orbital angular momenta and bonding characters of the orbitals containing electron spin. While Ti(C6H6)2 was found to be nonmagnetic, Tin(C6H6)n+1 (n = 2, 3) possess nonzero magnetic moments. The mechanism of ferromagnetic spin ordering in M2(C6H6)3 (M = Sc, Ti, V) is discussed qualitatively in terms of molecular orbital analysis. These sandwich species represent a new class of one-dimensional molecular magnets in which the transition-metal atoms are formally zerovalent.     

Structural, electronic, and magnetic properties of Con(benzene)m complexes

The structural, electronic, and magnetic properties of cobalt-benzene complexes (Co(n)Bz(m), n, m = 1-4, m = n, n + 1) have been explored within the framework of an all electron gradient-corrected density functional theory. Sandwich conformations are energetically preferred for the smallest series of n, m = 1-2, rice-ball structures are for larger sizes with n > or = 3, and both motifs coexist for Co(2)Bz(3). The rice-ball clusters of (3, 3) and (4, 4) are more stable than (3, 4) having a relative large binding energy and HOMO-LUMO gap whereas smaller sandwich clusters have highly kinetic stability at (n, n + 1). The computed ionization potentials and magnetic moments of Co(n)Bz(m) are in good agreement with the measured values overall; the present results suggest that the measured moments are averages reflecting mixtures of a few nearly isoenergetic isomers having different spin states. The magnetism of the complexes mainly comes from Co atoms with a Bz molecule only possessing very small moments. Ferromagnetic ordering is energetically preferred for smaller complexes with n = 1-3 whereas antiferromagnetic ordering is favored for (4, 4). The relatively smaller moments of Con clusters in a Bz matrix indicate that Bz molecules play an attenuation role to the magnetism of the complexes.     

Geometries and magnetisms of the Zr(n) (n=2-8) clusters: the density functional investigations

The geometries, stabilities, and electronic and magnetic properties of small-sized Zr(n) (n=2-8) clusters with different spin configurations were systematically investigated by using density functional approach. Emphasis is placed on studies that focus on the total energies, equilibrium geometries, growth-pattern behaviors, fragmentation energies, and magnetic characteristics of zirconium clusters. The optimized geometries show that the large-sized low-lying Zr(n) (n=5-8) clusters become three-dimensional structures. Particularly, the relative stabilities of Zr(n) clusters in terms of the calculated fragmentation energies and second-order difference of energies are discussed, exhibiting that the magic numbers of stabilities are n=2, 5, and 7 and that the pentagonal bipyramidal D(5h) Zr(7) geometry is the most stable isomer and a nonmagnetic ground state. Furthermore, the investigated magnetic moments confirm that the atomic averaged magnetic moments of the Zr(n) (n not equal to 2) display an odd-even oscillation features and the tetrahedron C(s) Zr(4) structure has the biggest atomic averaged magnetic moment of 1.5 mu(B)/at. In addition, the calculated highest occupied molecular orbital-lowest unoccupied molecular orbital gaps indicate that the Zr(n) (n=2 and 7) clusters have dramatically enhanced chemical stabilities.     

Geometric and magnetic properties of Pt clusters supported on graphene: relativistic density-functional calculations

The geometric and magnetic structures of small Pt(n) clusters (n = 1 - 5) supported on a graphene layer have been investigated using ab initio density functional calculations including spin-orbit coupling. Pt-Pt interactions were found to be much stronger than the Pt-C interactions promoting the binding to the support. As a consequence, the equilibrium structure of the gas-phase clusters is preserved if they are deposited on graphene. However, the clusters bind to graphene only via at most two Pt-C bonds: A Pt(2) dumbbell prefers an upright position, the larger clusters are bound to graphene only via one edge of the planar cluster (Pt(3) and Pt(5)) or via two terminal Pt atoms of a bent Pt(4) rhombus. Evidently, the strong buckling of the graphene layer induced by the Pt-C bonds prevents the formation of a larger number of cluster-support bonds. As the local spin and orbital magnetic moments are quenched on the Pt atoms forming Pt-C bonds, the magnetic structure of the supported clusters is much more inhomogeneous as in the gas-phase. This leads to noncollinear magnetic structures and a strongly reduced magnetic anisotropy energy.     

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.     

Ge_nEu(n=1-13)团簇的结构、电子及磁性质(英文)

利用密度泛函理论在广义梯度近似下研究了GenEu(n=1-13)团簇的生长模式和磁性.结果表明:对于GenEu(n=1-13)团簇的基态结构而言,没有Eu原子陷入笼中.这和SinEu以及其它过渡金属掺杂半导体团簇的生长模式不同.除GeEu团簇外,GenEu(n=2-13)团簇的磁矩均为7μB.团簇的总磁矩与Eu原子的4f轨道磁矩基本相等.Ge、Eu原子间的电荷转移以及Eu原子的5d、6p和6s间的轨道杂化可以增强Eu原子的局域磁矩,却不能增强团簇总磁矩.     

Magnetic Anisotropy of Small Ir<Subscript>n</Subscript> Clusters (n = 2–5)

We employ a noncollinear implementation of density functional theory (DFT) including spin–orbit coupling (SOC) interaction to calculate the magnetic properties of Ir_n (n = 2–5) clusters. The impact of the magnetic anisotropy on the geometric structures and magnetic properties has been analyzed. SOC leads to formation of large orbital moment and a mixing of different spin states, but does not affect the relative stability of different structural isomers for a given cluster. In order to measure the SOC effect, we further define the spin–orbit energy (E_so) and compute the exact values. Magnetic anisotropy energies (MAEs) obtained from DFT calculations are further supported by the results of torque approach. We find that MAEs of Ir₂ and Ir₃ in ground state configurations are 40.6 and 28.5 meV respectively, while the MAE decreases to 9 meV for Ir₄. For Ir₅, MAE for its ground state structure increases to 38.3 meV.     

Stern-gerlach study of multidecker lanthanide-cyclooctatetraene sandwich clusters

Multilayer lanthanide-cyclooctatetraene organometallic clusters, Lnn(C8H8)m (Ln = Eu, Tb, Ho, Tm; n = 1-7; m = n - 1, n, n + 1) were produced by a laser vaporization synthesis method. The magnetic deflections of these organometallic sandwich clusters were measured by a molecular beam magnetic deflection technique. Most of the sandwich species displayed one-sided deflection, while some of smaller Ln-C8H8 clusters showed symmetric broadening without or with only very small (or absent) net high-field deflection. In general, the total magnetic moments, calculated from the magnitude of the beams deflections, increase with the number of lanthanide atoms (i.e., with increasing sandwich layers); however for Tb-, Ho-, and Tm-C8H8 clusters with n > 3, the suppression of the magnetic moments was observed, possibly through antiferromagnetic interactions. For Eu-C8H8 clusters, we observe a linear increase of the magnetic moments with the number of Eu atoms up to n = 7, with average magnetic moment per Eu atom around 7 muB--similar to that displayed by conventionally synthesized mononuclear EuIIC8H8 complexes, indicating that Eu atoms exist as Eu2+ ions in the full sandwich Eun(C8H8)n+1 clusters. These results suggest that Eun(C8H8)n+1 is a promising candidate for a high-spin, one-dimensional building block in organometallic magnetic materials.     

Magnetic structure variation in manganese-oxide clusters

Negative-ion photoelectron spectroscopy and ab initio simulations are used to study the variation in magnetic structure in Mn(x)O(y) (x = 3, 4[semicolon] y = 1, 2) clusters. The ferrimagnetic and antiferromagnetic ground-state structures of Mn(x)O(y) are 0.16-1.20 eV lower in energy than their ferromagnetic isomers. The presence of oxygen thus stabilizes low-spin isomers relative to the preferred high-spin ordering of bare Mn(3) and Mn(4). Each cluster has a preferred overall magnetic moment, and no evidence is seen of competing states with different spin multiplicities. However, non-degenerate isomags, which possess the same spin multiplicity but different arrangements of local moments, do contribute additional features and peak broadening in the photoelectron spectra. Proper accounting for all possible isomags is shown to be critical for accurate computational prediction of the spectra.     

Deposition Morphology and Magnetism of Co,Pt Adatoms and Small CoPt Adclusters on Ni(100) Substrate

Theoretical calculations of Co\(_{n-x}\)Pt\(_x\) (n = 1–3; \(x \le n\)) clusters on Ni(100) surface for their spin and orbital magnetic moments, as well as the magnetic anisotropy energy (MAE), are performed by using the density-functional theory (DFT) method including a self-consistent treatment of spin–orbit coupling (SOC). The results reveal that the ferromagnetic Co atoms in intra Co\(_{n-x}\)Pt\(_x\) adclusters couple ferromagnetically to their underlayer Ni atoms. The predominant inter-interactions between Co adatoms and Ni surface with the partly filled 3d band, together with the secondary intra-interactions between Co adatoms and Pt adatoms with fully filled 5d band, lead to a strongly quenched orbital moment (\(\mu _{\mathrm{{orb}}}^{\mathrm{{Co}}}\) = 0.18–0.14 \(\mu _B\); \(\mu _{\mathrm{{orb}}}^{\mathrm{{Pt}}} \approx \) 0.24–0.19 \(\mu _B\)) but a less quenched spin moment (\(\mu _{\mathrm{{spin}}}^{\mathrm{{Co}}} \approx \) 2.0 \(\mu _B\); \(\mu _{\mathrm{{spin}}}^{\mathrm{{Pt}}} \approx \) 0.35 \( \mu _B\)). The MAEs of CoPt adclusters exhibit a strong dependence on alloying effect rather than size effect, which is direly proportional to SOC strength and orbital moment anisotropy. The oxidations of CoPt clusters always reduce orbital magnetic moments and consequently decrease the corresponding MAEs.     

TbSin(n=2-13)团簇的结构、电子及磁学性质

利用相对论密度泛函理论在广义梯度近似下研究TbSi_n (n=2-13)团簇的结构、稳定性、电子和磁学性质. 对团簇的平均结合能、离解能、电荷转移、最高占据分子轨道(HOMO)和最低未占据分子轨道(LUMO)的能级差、Mulliken 电荷分析和磁学性质进行了计算和讨论. TbSi_n团簇并没有像实验推测的那样在n=10形成嵌入式的结构. 我们推断电子亲和势的急剧变化不仅与嵌入式的结构有关, 而且与电子的固有稳定性相关.Mulliken 电荷分析表明电荷总是从Tb 原子转向Si 原子. 团簇的磁矩主要局域在Tb 原子的周围, 并且主要由f电子贡献, f 电子表现出局域性并且不参与化学成键. 以TbSi₁₀为例的分波态密度分析表明Tb与Si 原子间存在很强的sp轨道杂化.     

Density-functional study of small neutral and cationic bismuth clusters Bi(n) and Bi(n) (+)(n=2-24)

Density-functional theory with scalar-relativistic pseudopotential and a generalized gradient correction is used to calculate the neutral and cationic Bi(n) clusters (2< or =n< or =24), with the aim to elucidate their structural evolution, relative stability, and magnetic property. The structures of neutral Bi clusters are found to be similar to that of other group-V elemental clusters, with the extensively studied sizes of n=4 and 8 having a tetrahedron and wedgelike structure, respectively. Generally, larger Bi clusters consist of a combination of several stable units of Bi(4), Bi(6), and Bi(8), and they have a tendency to form an amorphous structure with the increase of cluster sizes. The curves of second order energy difference exhibit strong odd-even alternations for both neutral and cationic Bi clusters, indicating that even-atom (odd-atom) sizes are relatively stable in neutral clusters (cationic clusters). The calculated magnetic moments are 1micro (B) for odd-atom clusters and zero for even-atom clusters. We propose that the difference in magnetism between experiment and theory can be greatly improved by considering the orbital contribution. The calculated fragmentation behavior agrees well with the experiment, and for each cationic cluster the dissociation into Bi(4) or Bi(7) (+) subclusters confirms the special stability of Bi(4) and Bi(7) (+). Moreover, the bond orders and the gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital show that small Bi clusters would prefer semiconductor characters to metallicity.     

Photoelectron spectroscopic study of iron-pyrene cluster anions

Iron-pyrene cluster anions, [Fe(m)(pyrene)(n)](-) (m = 1-2, n = 1-2) were studied in the gas phase by photoelectron spectroscopy, resulting in the determination of their electron affinity and vertical detachment energy values. Density functional theory calculations were also conducted, providing the structures and spin multiplicities of the neutral clusters and their anions as well as their respective electron affinity and vertical detachment energy values. The calculated magnetic moments of neutral Fe(1)(pyrene)(1) and Fe(2)(pyrene)(1) clusters suggest that a single pyrene molecule could be a suitable template on which to deposit small iron clusters, and that these in turn might form the basis of an iron cluster-based magnetic material. A comparison of the structures and corresponding photoelectron spectra for the iron-benzene, iron-pyrene, and iron-coronene cluster systems revealed that pyrene behaves more similarly to coronene than to benzene.     

(CoMn)n(n=1～5)合金团簇的结构和磁性

All geometry structures of (CoMn)n (n=1-5) clusters were optimized, and the energy, frequence and magnetism of (CoMn)n (n=1-5) clusters were calculated by using the local spin density approximation and generalized gradient approximation of density functional theory. The same ground state structures of CoMn alloy clusters were confirmed in two methods, and magnetism of CoMn alloy ground state clusters was studied systemically. In order to understand structure and magnetism of CoMn alloy clusters better, Co2n (n=1-5) and Mn2n (n=1-5) clusters were calculated by the same method as alloy clusters, whose ground state structure and magnetism were confirmed. Moreover, the ground state structure and magnetism of clusters with the corresponding CoMn alloy clusters was compared. Results indicated that for (CoMn)n (n=1-4) clusters, geometry structures of CoMn alloy clusters are the same as the corresponding pure clusters still, (CoMn)3 and (CoMn)4 exhibit magnetic bistability, show ferromagnetic and anti-ferromagnetic coupling, local magnetic moment of Co, Mn atoms in CoMn alloy clusters almost preserves magnetism of pure clusters still.     

Electron solvation in water-ammonia mixed clusters: Structure, energetics, and the nature of localization states of the excess electron

The structure and energetics of water-ammonia mixed clusters with an excess electron, [(H2O)n(NH3)m]- with m=1, n=2-6 and m=2, n=2, and also the corresponding neutral clusters are investigated in detail by means of ab initio quantum chemical calculations. The authors focus on the localization structure of the excess electron with respect to its surface versus interiorlike states, its binding to ammonia versus water molecules, the spatial and orientational arrangement of solvent molecules around the excess electron, the changes of the overall hydrogen-bonded structure of the clusters as compared to those of the neutral ones and associated dipole moment changes, vertical detachment energies of the anionic clusters, and also the vertical attachment energies of the neutral clusters. It is found that the hydrogen-bonded structure of the anionic clusters are very different from those of the neutral clusters unlike the case of water-ammonia dimer anion, and these changes in structural arrangements lead to drastically different dipole moments of the anionic and the neutral clusters. The spatial distribution of the singly occupied molecular orbital holding the excess electron shows only surface states for the smaller clusters. However, for n=5 and 6, both surface and interiorlike binding states are found to exist for the excess electron. For the surface states, the excess electron can be bound to the dangling hydrogens of either an ammonia or a water molecule with different degrees of stability and vertical detachment energies. The interiorlike states, wherever they exist, are found to have a higher vertical detachment energy than any of the surface states of the same cluster. Also, for interiorlike states, the ammonia molecule with its dangling hydrogens is always found to stay on top or on a far side of the charge density of the excess electron without participating in the hydrogen bond network of the cluster; the intermolecular hydrogen bonds are formed by the water molecules only which add to the overall stability of these anionic clusters.     

Nickel and copper doped palladium clusters from a first-principles perspective

A complete study on the evolution of structures and the variation of the energy properties of MPd_n−1 (M = Ni and Cu; n = 2-13) clusters is presented. The study was performed employing auxiliary density functional theory. The obtained results were compared with the results of Pd_n clusters studied with the same methodology. For each cluster size, several structures were studied to determine the lowest energy structures. The initial structures for the geometry optimization were taken along ab initio Born-Oppenheimer molecular dynamics trajectories. Different potentials energy surfaces were studied. All cluster structures were fully optimized without any symmetry restriction. Stable structures, frequencies, spin multiplicities, averaged bond lengths, spin density plots, different energy properties, dipole and magnetic moments as well as charge transfers are reported. This investigation indicates that the palladium clusters doped with a Ni atom are the most stable and potentially the most chemical active ones.     

Computational investigation of TiSin (n=2-15) clusters by the density-functional theory

The geometries, stabilities, and electronic properties of TiSin (n=2-15) clusters with different spin configurations have been systematically investigated by using density-functional theory approach at B3LYP/LanL2DZ level. According to the optimum TiSin clusters, the equilibrium site of Ti atom gradually moves from convex to surface, and to a concave site as the number of Si atom increases from 2 to 15. When n=12, the Ti atom in TiSi12 completely falls into the center of the Si outer frame, forming metal-encapsulated Si cages, which can be explained by using 16-electron rule. On the basis of the optimized geometries, various energetic properties are calculated for the most stable isomers of TiSin clusters, including the average binding energy, the highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO-LUMO) gap, fragmentation energy, and the second-order difference of energy. It is found that at size n=6,8,12 the clusters are more stable than neighboring ones. According to the Mulliken charge population analysis, charges always transfer from Si atoms to Ti atom. Furthermore, the HOMO-LUMO gaps of the most stable TiSin clusters are usually smaller than those of Sin clusters.     

用密度泛函理论研究ZrnB(n=1-13)团簇的结构及性质

利用密度泛函理论, 得到了ZrnB(n=1-13)团簇的基态结构, 计算并讨论了团簇能量的二阶差分和离解能. 结果表明, n=2, 5, 12时, 相应团簇较稳定, 特别是Zr5B团簇的稳定性最高. 同时分析了ZrnB团簇的电子性质及磁性, 结果显示能隙随n值的增大出现奇偶振荡趋势, 特别是Zr12B团簇的能隙只有0.015 eV, 表明该团簇已具有金属性. 电荷转移随n值增大, 整体呈增大趋势, 除了二聚体ZrB, 电荷由B原子转移到Zr原子. 利用Mulliken布居分析得到二聚体ZrB(5.000 μB)和团簇Zr4B(3.000 μB)的磁矩较大, ZrnB团簇中总磁矩主要来自Zr原子的4d轨道.     

A density functional study of YnAl (n=1-14) clusters

The geometries, stabilities, and electronic and magnetic properties of Y(n)Al (n=1-14) clusters have been systematically investigated by using density functional theory with generalized gradient approximation. The growth pattern for different sized Y(n)Al (n=1-14) clusters is Al-substituted Y(n+1) clusters and it keeps the similar frameworks of the most stable Y(n+1) clusters except for Y(9)Al cluster. The Al atom substituted the surface atom of the Y(n+1) clusters for n<9. Starting from n=9, the Al atom completely falls into the center of the Y-frame. The Al atom substituted the center atom of the Y(n+1) clusters to form the Al-encapsulated Y(n) geometries for n>9. The calculated results manifest that doping of the Al atom contributes to strengthen the stabilities of the yttrium framework. In addition, the relative stability of Y(12)Al is the strongest among all different sized Y(n)Al clusters, which might stem from its highly symmetric geometry. Mulliken population analysis shows that the charges always transfer from Y atoms to Al atom in all different sized clusters. Doping of the Al atom decreases the average magnetic moments of most Y(n) clusters. Especially, the magnetic moment is completely quenched after doping Al in the Y(13), which is ascribed to the disappearance of the ininerant 4d electron spin exchange effect. Finally, the frontier orbitals properties of Y(n)Al are also discussed.     

Symmetry and ferromagnetic clusters

Isomers of pure Fe₁₃ and icosahedral Fe₁₂X clusters are studied using the all-electron linear-combination-of-Gaussian-type-orbital (LCGTO) local-density-functional (LDF) methods that allow the spin and geometry of the cluster to be determined self-consistently. The Fe₁₃ ground state is icosahedral. The icosahedral cluster also has the greatest magnetic moment because of increased symmetry-required orbital degeneracy for electrons of different spins. The central atom of the icosahedral iron cluster has been varied to optimize the spin of the cluster keeping the oribital contribution to the magnetic moment quenched. Varying the central atom under this constraint can alter the magnetic moment by more than 20%. Similar studies have begun on 55-atom icosahedral iron clusters.