Helium clusters at finite temperature

An analysis of helium cluster properties at finite temperature using a phenomenological free energy density has been carried out. We have studied in detail the energetics and the density profile characteristics of hot drops of both helium isotopes containing 70, 112, 168, 240 and 330 atoms. A finite temperature mass formula including volume, surface and curvature terms has been derived.     

Stability and structure of singly-charged argon clusters Ar n + ,n=3–27. A Monte-Carlo simulation

Monte-Carlo calculations have been performed for positively charged argon clusters in the temperature range between 10 K and 40 K using two different models (one with a dimer ion core, the other one with a trimer ion). The argon-argon interaction potential stems from empirical data, the ion-neutral atoms potential is determined by ab initio MRD-CI calculations. Special stability is found for clusters sizesn=13, 19, 23 and 25/26 atoms using the ‘trimeric core model’ and for those withn=14,n=17,n=20 using the ‘dimeric core model’. The geometrical structure of the clusters is given and the construction principles are discussed in light of the interactions among neutral argon atoms and the ion-neutral atoms interaction.     

On the stability of Pb n m+ -clusters

The stability of multiply charged Pb _n ^m+ -clusters (n ≤ 3;m=0, 1, 2) was studied by solving exactly for the valencep-electrons a many body Hubbard-like Hamiltonian with intra- and interatomic Coulomb interactions. Particularly we obtain that Pb ₃ ²⁺ has a metastable ground state, in which Pb ₃ ²⁺ has isosceles shape (bond lengthR=3.2 Å, bond angle θ=124°) and a positive binding energyE _B =3.4 eV. The activation barrier against dissociation into Pb ₂ ⁺ + Pb⁺ is 0.13 eV, yielding a very long lifetime. This is in agreement with recent experiments [1] in which the lifetime of Pb ₃ ²⁺ was determined to be at least 10^?6 s. Comparison with self consistent Hartree-Fock calculations shows that the metastability of Pb ₃ ²⁺ is due to electronic correlations within the paramagnetic ground state.     

Structure and stability for (AlN) n + and (AlN) n + (n=1–15) clusters

Using density functional theory (DFT) method with 6-31G* basis set, we have carried out the optimizing calculation of geometry, vibrational frequency and thermodynamical stability for (AlN) _n ⁺ and (AlN) _n ⁺ (n=1–15) clusters. Moreover, their ionic potential (IP) and electron affinity (EA) were discussed. The results show that the electrical charge condition of the cluster has a relatively great impact on the structure of the cluster and with the increase of n, this kind of impact is reduced gradually. There are no Al-Al and N-N bonds in the stable structure of (AlN) _n ⁺ or (AlN) _n ^-, and the Al-N bond is the sole bond type. The magic number regularity of (AlN) _n ⁺ and (AlN) _n ^- is consistent with that for (AlN) _n , indicating that the structure with even n such as 2, 4, 6, ... is more stable. In addition, (AlN₁₀ has the maximal ionization power (9.14 eV) and the minimal electron affinity energy (0.19 eV), which manifests that (AlN)₁₀ is more stable than other clusters.     

Electronic structure and stability of AlnPn (n = 2-4) clusters

The geometry, electronic configurations, harmonic vibrational frequencies, and stability of the structural isomers of aluminum phosphide clusters have been investigated using the density functional theory. For dimers and trimers, the lowest energy structures are cyclic (IIs, IIIs) with D(nh) symmetry. The caged structure with Td symmetry (Xs) lie lowest in energy among the tetramers. The Al--P bond dominates the structures for many isomers so that one preferred dissociation channel is loss of the AlP monomer. The hybridization and chemical bonding in the different structures are also discussed. Comparisons with silicon and boron nitride clusters, the ground state structures of Al(n)P(n) clusters are analogous to those of their corresponding Si(2n) counterparts. This similarity follows the isoelectronic principle.     

Spectral shifts and structures of phenol...Ar(n) clusters

A laser spectroscopic investigation of phenol...Ar(n) (n = 1-6) clusters in the first electronically excited state (S(1)) and the cationic ground state (D(0)) is reported. Resonance enhanced two-photon ionisation (R2PI) spectra have been recorded for the investigation of the S(1) state. The origins of S(1)← S(0) (S(1)0(0)) transition of phenol...Ar(n) (n = 1, 2,4-6) are all red shifted compared to the S(1)0(0) state of the monomer by 33 cm(-1), 67 cm(-1), 10 cm(-1), 20 cm(-1), 44 cm(-1), respectively. However, the origin of the phenolAr(3) cluster is blue shifted by 25 cm(-1). For the investigation of the ionic ground state photoionization efficiency (PIE) and mass-analyzed-threshold ionization (MATI) spectroscopy have been applied. The spectra of phenol...Ar(3) and phenol...Ar(4) yield values for the ionization energy (IE) of 68,077 ± 15 cm(-1) and 67,948 ± 15 cm(-1). With the combination of theoretical methods and R2PI, PIE and MATI spectroscopy, the major species present have been positively identified.     

Structure and stability of (AlN)n clusters

AIN and Al2N2 have been observed in the record of time-of-flight mass-spectra as positive ions. Associating with density functional theory(DFT) B3LYP method with 6-31G* basis set, we have carried out the optimizing calculations of the geometry, electronic state and vibrational frequency for (AIN)n (n = 1-15) clusters, moreover, discussed the character of the chemical bond and thermodynamical stability and explained the experimental mass spectra. The results show that there do not exist AI-AI and N-N bonds and only exists AI-N bond in the ground state structures of (AIN)n clusters; and the "magical number" regularity of (AIN)n is those whose atom number Is 4, 8, 12,16, 20, etc, all of which are times of four.     

Predicted stability and structure of (HXeCCH)n (n=2 or 4) clusters and of crystalline HXeCCH

Ab initio calculations predict the existence of the dimer and tetramer of HXeCCH. The interaction energies are -6.66 and -19.40 kcal mol-1 for the dimer and tetramer, respectively. For both complexes, larger blue shifts of the Xe-H stretching mode are found, while the Xe-C stretching modes are slightly redshifted. The stability and structure of HXeCCH crystals is predicted by density functional theory calculations with periodic boundary conditions. Strong electrostatic interactions are found between the monomers in the crystal. The results are first evidence for the existence of crystalline materials made of a novel class of noble gas molecules.     

On the Lindemann criterion for quantum clusters at very low temperature

The Lindemann criterion to discern the solid-like or liquid-like nature of a quantum cluster at T = 0 is discussed. A critical analysis of current Lindemann parameters is presented and a new parameter is proposed that is appropriate to study quantum clusters made of identical particles. A simple model wave function is introduced to fix the range of variation of these parameters. The model presents two extreme limits that correspond to either a liquid-like or a solid-like system; besides, it fulfills the Bose symmetry and also permits evaluations without symmetrization. Variational and diffusion Monte Carlo calculations are also performed for clusters of spinless bosons interacting through Lennard-Jones potentials. It is shown that the liquid-like or solid-like character of quantum clusters at zero temperature cannot be simply established in terms of a single parameter.     

Structure and stability of B+13 clusters

The structures and energies of B⁺₁₃, observed experimentally to be an unusually abundant species among cationic boron clusters, have been studied systematically with B3LYP/6–31G* density functional theory. The most thermodynamically stable B⁺₁₂ and B⁺₁₃ clusters are confirmed to have planar or quasiplanar rather than globular structures. However, the computed dissociation energies of the 3-dimensional B⁺₁₃ clusters are much closer to the experimental values than those of the planar or quasiplanar structures. Hence, planar and 3-dimensional B⁺₁₃ may both exist. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 203–214, 1998     

Theoretical study of the electronic structure and stability of titanium dioxide clusters (TiO2)n with n = 1-9

The electronic structure and the stability of both neutral and singly charged (TiO2)n clusters with n = 1-9 have been investigated using the density functional B3LYP/LANL2DZ method. The lowest-lying singlet clusters tend to form some compact structures with one or two terminal Ti-O bonds, which are about 1.4-2.5 eV more stable than the corresponding triplet structures. For the lowest-lying structures, strong infrared absorption lines at 988-1020 cm(-1) due to terminal Ti-O bonds and below 930 cm(-1) due to Ti-O-Ti bridging bonds may be observed, with some characteristic lines at 530-760 cm(-1) due to 3-fold coordinated O-atoms that are comparable with the spectra of rutile and anatase bulk. The holes and excited electrons within triplet structures tend to be localized on the least coordinated O- and Ti-atoms, respectively, with some exceptions possibly due to the electron-hole interaction. The extra electrons within (TiO2)n- clusters and the holes within (TiO2)n+ clusters show a clearer preference of location on the least coordinated Ti- and O-atoms, respectively. For the lowest-lying (TiO2)n clusters, the cluster formation energy per TiO2 unit and the electron affinity tend to increase whereas the ionization potential tends to decrease with the cluster size n. On the other hand, the singlet-triplet and HOMO-LUMO gaps represent the lower and upper limits of the TiO2 bulk band gaps, respectively. The theoretical results agree well with the available experimental data and may be helpful for understanding the chemistry of small (TiO2)n clusters.     

Evaporation of tetramers in Sb4n clusters and conditions for the formation of Sb2n+1 clusters

Antimony clusters are produced by the inert gas condensation technique. They are found to be built from Sb₄ units. The fragmentation by evaporation of Sb₄ units is studied as a function of the excess energy in the cluster. By this way the binding energy of the Sb₄ units in the cluster is found to be about 1.5 eV, well below the binding energy of a Sb atom in the bulk and in Sb₄(?3eV). The evolution of ionization potentials of Sb_4n clusters confirms that their structure is probably non metallic. Finally the possible metastable character of this Sb_4n structure is discussed.     

Surface structure and stability of MoSx model clusters

Density functional theory (DFT) computations have been carried out to study the structure and stability of MoSx clusters with the change of sulfur coverage at both Mo and S edges. DFT shows that adding sulfur to the Mo edge is always exothermic. However, deleting corner sulfur from the S edge is exothermic for 67 and 50% sulfur coverages, while deleting edge sulfur from the S edge is endothermic for 33 and 0% sulfur coverages. On the basis of the computed free energies along a wide range of H2S/H2 ratios, it is found that there are two stable structures with 33 and 50% sulfur coverages on the Mo edge by having 100% sulfur coverage on the S edge and one stable structure with 67% sulfur coverage on the S edge by having 0% sulfur coverage on the Mo edge. Under fully sulfiding atmosphere or at a very high H2S/H2 ratio, triangle MoSx structures with 100% sulfur coverage on the Mo edge are computed to be more stable than those with 100% sulfur coverage on the S edge, in agreement with the observation of scanning tunneling microscopy. In addition, the effects of cluster sizes on the surface structures are discussed.     

Electronic structure and stability of charged beryllium clusters

Electronic structure studies on neutral, singly and doubly ionized Be _n clusters (n≤5) have been carried out in order to investigate the stability and observability of charged clusters. Our studies employ wave function expansion in terms of gaussian type orbitals and have been carried out within local spin density formalism. It is shown that although small doubly ionized clusters are unstable, they are protected from fragmentation by energy barriers. We illustrate this explicitly for trimers by presenting a Born-Oppenheimer surface of Be₃, Be ₃ ⁺ and Be ₃ ⁺⁺ . It is argued that depending on their geometries, the observable doubly charged clusters can be generated through a one or two photons ionization. We also present results on the distribution of “hole charge” in doubly ionized clusters and show that a small cluster exhibits metallic like behaviour in regard to distribution of missing electronic charge.     

Time resolved photofragmentation of Au n + and Ag n + clusters (n = 9, 21)

Gold and silver cluster ions were produced by laser vaporization and stored in a Penning trap. After mass selection the cluster sizes of interest were illuminated by a laser pulse and electronically excited. Photoabsorption cross sections and fragmentation patterns were measured for photon energies of 2.3 eV to 5.2 eV. Unimolecular dissociation was observed time resolved on a microsecond to millisecond scale. Dissociation energies were deduced from the measured life times.     

Structure and stability of (A1N)n clusters

AIN and AI₂N₂ have been observed in the record of time-of-flight mass-spectra as positive ions. Associating with density functional theory(DFT) B3LYP method with 6-31G* basis set, we have carried out the optimizing calculations of the geometry, electronic state and vibrational frequency for (AIN)_n (n = 1—15) clusters, moreover, discussed the character of the chemical bond and thermodynamical stability and explained the experimental mass spectra. The results show that there do not exist AI-AI and N-N bonds and only exists Al-N bond in the ground state structures of (AIN)_n clusters; and the “magical number” regularity of (AIN)_n is those whose atom number is 4, 8, 12, 16, 20, etc, all of which are times of four.