Atomic clusters, consisting of a few to a few thousand atoms, have emerged over the past 40 years as the ultimate nanoparticles, whose structure and properties can be controlled one atom at a time. One of the early motivations in studying clusters was to understand how the properties of matter evolve as a function of size, shape, and composition. Over the past few decades, more than 200 000 papers have been published in this field. These studies have not only led to a considerable understanding of this evolution from clusters to crystals, but also have revealed many unusual size-specific properties that make cluster science an interdisciplinary field on its own, bridging physics, chemistry, materials science, biology, and medicine. More importantly, the possibility of creating a new class of materials, composed of clusters instead of atoms as building blocks, has fueled the hope that one can synthesize materials from the bottom-up with unique and tailored properties. This Review focuses on the properties ...

Super Atomic Clusters: Design Rules and Potential for Building Blocks of Materials

The equilibrium bond lengths, harmonic vibrational frequencies, and dissociation energies of the ground state homonuclear 3d transition-metal diatomics (scandium through copper) were determined using six density functional or hybrid Hartree–Fock/density functional theory (HF/DFT) methods and unrestricted Hartree–Fock theory. Results are compared to other theoretical studies and to experimental values when available. The accuracy of the DFT results is found to be highly dependent upon the functional employed, with the pure DFT methods, BLYP and BP86, often performing significantly better than the hybrid HF/DFT methods. For the van der Waals complex Mn2, all six functionals predict the ground state to be high-spin, disagreeing with experiment; the true (antiferromagnetic) ground state was not found for any functional. Average errors for theoretical geometries and vibrational frequencies are for B3LYP, 0.053 A (2.4%) and 122 cm−1 (31.1%); for B3P86, 0.051 A (2.4%) and 122 cm−1 (31.3%); for BHLYP, 0.077 A (4.1%) and 208 cm−1 (49.3%); for BLYP, 0.024 A (1.3%) and 98 cm−1 (24.5%); for BP86, 0.020 A (1.1%) and 104 cm−1 (25.6%); and for LSDA, 0.056 A (3.0%) and 158 cm−1 (37.9%). No functional gives results directly comparable for all nine species. Dissociation energy results are severely overestimated in many instances and negative in others. Anecdotal reports of success for density functional theory for these systems may have been overblown.

Homonuclear 3d transition-metal diatomics: A systematic density functional theory study

The interaction of $3d$ transition metal atoms and dimers with a single-walled armchair carbon nanotube has been investigated by first-principles density functional calculations. For Fe-, Co-, and Ni-doped (4,4) nanotubes, outside adsorption sites are the most favorable. The interactions are largely ferromagnetic for Fe and Co, with the local magnetic moments of the dimers being similar to the free dimers. However, for Ni most structures are nonmagnetic. We have also examined the effects of curvature with calculations for graphene and the (8,8) nanotube. For the (8,8) nanotube, the interaction of Co becomes more favorable inside the nanotube. Doping of a single Co atom transforms the (4,4) and (8,8) nanotubes into half-metals. These results are useful for spintronics applications and could help in the development of magnetic nanostructures and metallic nanotube coatings.

Stable geometries and magnetic properties of single-walled carbon nanotubes doped with 3d transition metals: A first-principles study

Isolated manganese clusters, ${\text{Mn}}_{n},\phantom{\rule{0.3em}{0ex}}(n=5--22)$ are deflected by a linear-gradient magnetic field. ${\text{Mn}}_{7}{\text{\ensuremath{-}}\text{Mn}}_{22}$ are found to deflect uniformly toward high field. The magnitude of the deflections indicate susceptibilities far in excess of those expected based on the susceptibility of bulk manganese, demonstrating that Mn clusters in this size range are magnetically ordered. Per-atom moments obtained from Curie's Law analysis range from $0.4{\ensuremath{\mu}}_{b}\phantom{\rule{0.3em}{0ex}}({\text{Mn}}_{19})$ to $1.7\phantom{\rule{0.3em}{0ex}}{\ensuremath{\mu}}_{b}\phantom{\rule{0.3em}{0ex}}({\text{Mn}}_{12})$. For ${\text{Mn}}_{5}$ and ${\text{Mn}}_{6}$, symmetric broadening of the cluster beam is observed, and their moments were determined via line-shape analysis using both free-spin and adiabatic rotor models. The measured moments, interpreted in light of recent density functional theory calculations, suggest that Mn clusters in this size range are molecular ferrimagnets.

Magnetic ordering in manganese clusters

We systematically investigate the structural, electronic, and magnetic properties of Mnn clusters n =2–2 0 within the ab initio pseudopotential plane wave method using generalized gradient approximation for the exchange-correlation energy. A new kind of icosahedral structural growth has been predicted in the intermediate size range. Calculated magnetic moments show an excellent agreement with the Stern-Gerlach experiment. A transition from ferromagnetic to ferrimagnetic Mn-Mn coupling takes place at n = 5 and the ferrimagnetic states continue to be the ground states for the entire size range. Possible presence of multiple isomers in the experimental beam has been argued. No signature of nonmetal to metal transition is observed in this size range and the coordination dependence of d-electron localization is discussed.

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Structure, electronic properties, and magnetic transition in manganese clusters

The equilibrium geometries, electronic structure and magnetic properties of small Mn clusters consisting of up to five atoms have been calculated self-consistently using first principles molecular orbital theory. The electron-electron interaction has been accounted for using the local spin density and generalized gradient approximation to the density functional theory. The atomic orbitals forming the molecular orbital have been represented separately by Gaussian and numerical basis sets. Two different computer codes (Gaussian 94 and DMOL) were used to check the numerical consistency of our calculations. is found to be a weakly bound van der Waals molecule and its binding energy depends sensitively on the choice of basis set as well as the form of the exchange-correlation potential. The binding energies are less sensitive to these approximations in larger clusters. The binding improves with cluster size, but remains significantly lower than those in other transition metal clusters. The equilibrium geometries are fairly compact and symmetric although other isomers with distorted geometries and with nearly the same energy as that of the ground state do exist for . The clusters also exhibit a variety of low-lying spin multiplicities, but the ground state spin configuration is ferromagnetic with a magnetic moment of . This not only contrasts with its bulk behaviour which is antiferromagnetic, but also differs from the behaviour in other transition-metal clusters where the magnetic moments/atom are always less than the free-atom value. The results are compared with available experiments on matrix isolated Mn clusters.

https://iopscience.iop.org/article/10.1088/0953-8984/10/48/009/pdf

S K Nayak

Papers

Equilibrium geometries, electronic structure and magnetic properties of small manganese clusters