Theory for the short-time response of small Hg n clusters after excitation

The short-time behavior of small Hg _n clusters immediately after single or double ionization is studied. We calculate self-consistently the ground state electronic energyE of ionized Hg _n clusters. Upon ionization changes of the potential energy surface (PES) occur, which govern the atomic motion in the cluster. These changes depend on cluster size and charge and are determined by the interplay between the localization of the holes within an ionic core and the polarization energy of the neutral rest of the cluster. In the case of single ionization of the cluster the PES results mainly from hole delocalization. In contrast, in the case of double ionization the PES is governed almost only by strong environment polarization. We use our theory to explain the physical origin of the oscillations in the ionization cross-section of singly and doubly excited Hg _n clusters observed in recent pump-probe experiments.     

A REMPI study of solvation of small Hg n clusters by polar molecules

Free Hg _n (DME) _m clusters (where DME=dimethyl-ether,n=1, 2, 3,m=1÷5) formed in a supersonic expansion were studied by the REMPI (Resonance-Enhanced Multi-Photon Ionization) technique. A large decrease of ionization energies due to solvation of Hg _n clusters is observed. Preliminary results are discussed in terms of different equilibrium configurations of the electronic ground, excited and ionic states of clusters.     

Structures and electronic properties of small FeB n (n=1-10) clusters

The geometries, stabilities, electronic properties, and magnetism of FeB(n) clusters up to n=10 are systematically studied with density functional theory. We find that our optimized structures of FeB(2), FeB(3), FeB(4), and FeB(5) clusters are more stable than those proposed in previous literature. The results show that it is favorable for the Fe atom to locate at the surface, not at the center of the cluster, and that FeB(4) and FeB(9) clusters exhibit high stability. For all the FeB(n) clusters studied, we find the charge transfer from Fe to B site and the coexistence of ionic and covalent bonding characteristics. The computed total magnetic moments of the lowest-energy structures oscillate with the cluster size and are quenched at n=4, 6, 8, and 10.     

Theory of nonlinear optical properties of small metallic spheres

We calculate the nonlinear optical properties of small metallic spheres using electromagnetic theory and assuming that the local response of the conduction electrons is the same as for a plane surface. Electromagnetic Mie-resonances cause a strong increase of the second and higher harmonics in the reflected light. Detailed results are given for the second and third harmonic generation, its dependence on the frequency and polarization of the incident light, and on the cluster size. An enhancement of the second harmonic generation by a factor of about 5000 is obtained for small spherical metallic clusters. This is in good agreement with experiments on artificially roughened metal surfaces.     

On the localization of electrons and holes in Hg n and rare-gas clusters

We have used a microscopic theory to study the size dependence of the degree of localization of the valence electrons and holes in neutral an ionized rare-gas-and Hg _n clusters. We discuss under which circumstances localization of the electrons and holes is favoured. We have calculated the ionization potential of Xe _n , Kr _n and small Hg _n clusters. Good agreement with experiments is obtained. We have also determined the dependence of the ionization potential on cluster structure.     

Theoretical investigation of the large nonlinear optical properties of (HCN)n clusters with Li atom

Two new classes of (HCN)(n)...Li and Li...(HCN)(n) (n = 1, 2, 3) clusters with the electride characteristic are formed in theory by the metal Li atom attaching to the (HCN)(n) (n = 1, 2, 3) clusters. Because of the interaction between the Li atom and the (HCN)(n) part, the 2s valence electron of the Li atom becomes a loosely bound excess electron. Our high-level ab initio calculations show that these new clusters with the excess electron have large first hyperpolarizabilities, for example, beta(0) = -15,258 au for (HCN)...Li and beta(0) = -3401 au for Li...(HCN) at the QCISD/6-311++G(3df,3pd) level (only beta(0) = -2.8 au for HCN monomer(26)). Obviously, the excess electron from the Li atom plays a crucial role in the large first hyperpolarizabilities of these clusters. The beta(0) value of (HCN)(n)...Li (beta(0) > 10(4) au, from sigma --> pi* transition) is larger than that of Li...(HCN)(n) (beta(0) > 10(3) au, from sigma --> sigma* transition) for n = 1, 2, or 3. In addition, two interesting rules have been observed. They are that |beta(0)| decreases with lengthening of the HCN chain for (HCN)(n)...Li clusters and that |beta(0)| increases as n increases for Li...(HCN)(n) clusters. In this paper, we discuss two classes of clusters that are highly similar to the electride structure model, of which the structural characteristics are that alkali metal atoms ionize to form cations and trapped electrons under the action of other polar molecules. Thus, the investigation on the large first hyperpolarizabilities of (HCN)(n)...Li and Li...(HCN)(n) (n = 1, 2, 3) may prompt one to study the unusual nonlinear optical responses of some electrides.     

Rydberg states of small NaAr(n)* clusters

The 4s and 5s Rydberg excited states of NaAr(n)* clusters are investigated using a pseudopotential quantum-classical method. While NaAr(n) clusters in their ground state are known to be weakly bound van der Waals complexes with Na lying at the surface of the argon cluster, isomers in 4s or 5s electronically excited states of small NaAr(n)* clusters (n< or =10) are found to be stable versus dissociation. The relationship between electronic excitation and cluster geometry is analyzed as a function of cluster size. For both 4s and 5s states, the stable exciplex isomers essentially appear as sodium-centered structures with similar topologies, converging towards those of the related NaAr(n)+ positive ions when the excitation level is increased. This is consistent with a Rydberg-type picture for the electronically excited cluster, described by a central sodium ion solvated by an argon shell, and an outer diffuse electron orbiting around this NaAr(n)+ cluster core.     

Theory for spin relaxation in small magnetic metal clusters

We discuss the magnetic properties of small neutral transition-metal clusters like Fe _n and Co _n deduced from Stern-Gerlach deflection experiments. We claim that the asymmetric Stern-Gerlach deflection profiles are due to a transfer from electronical angular momentum to the cluster rotation, allowing for a depopulation of the high energy magnetic levels. For finite temperatures we consider two limiting cases. First, the cluster magnetization is assumed to be tied to the random orientation of the cluster easy axes due to the lattice anisotropy. This causes a surprisingly small magnetization for small external magnetic fields. For larger fields and also for increasing temperatures the magnetization is released from the cluster geometry and allowed to align itself parallel to the field. In the second case the clusters are treated as an ensemble of superparamagnetic particles. Here, the effect of the anisotropy is less visible. The cluster lattice anisotropy per atom is expected to decrease for increasing cluster size. Preliminary results support this.     

Theoretical study of the electronic and optical properties of photochromic dithienylethene derivatives connected to small gold clusters

In the course of developing electronic devices on a molecular scale, dithienylethenes photochromic molecules constitute promising candidates for optoelectronic applications such as memories and switches. There is thus a great interest to understand and control the switching behavior of photochromic compounds deposited on metallic surfaces or nanoparticles. Within the framework of the density functional theory, we studied the effect of small gold clusters (Au3 and Au9) on the electronic structure and absorption spectrum of a model dithienylethene molecule. The molecular orbital interactions between the photochromic molecule and the gold cluster made it possible to rationalize some experimental findings (Dulic, D.; van der Molen, S. J.; Kudernac, T.; Jonkman, H. T.; de Jong, J. J. D.; Bowden, T. N.; van Esch, J.; Feringa, B. L.; van Wees, B. J. Phys. Rev. Lett. 2003, 91, 207402). For the closed-ring isomer, grafting a photochromic molecule on a small gold cluster does not change the characteristics of the electronic transition involved in the ring-opening reaction. On the opposite, the absorption spectrum of the photochromic open-ring isomer is strongly modified by the inclusion of the metallic cluster. In agreement with experimental results, our study thus showed that the cycloreversion reaction which involves the closed-ring isomer should be still possible, whereas the ring-closure reaction which involves the open-ring isomer should be inhibited. Connecting a dithienylethene molecule to a small gold cluster hence provides a qualitative comprehension of the photochromic activities of dithienylethenes connected to a gold surface.     

Theoretical study of optical properties of gold clusters

Characteristics of photoelectron spectrum of Au²⁻ and Au⁴⁻ clusters were calculated using different functionals and basis sets, and the results were compared with experimental data. The TD-B3LYP/LANL2Z method was shown to provide for calculation of these characteristics with good accuracy. Based on these results we suggested the methods and carried out appropriate calculations of the absorption and emission for different isomers of Au8 clusters. It was shown that the best agreement with the experimental data is observed for the planar C_2ν “hexagon+1” structure, therefore, this is the structure observed experimentally. The calculated value of the Stokes shift for the specified structure does not exceed 12 nm, which is also in good agreement with experimental results.     

Density functional study of structural, electronic, and optical properties of small bimetallic ruthenium-copper clusters

The structural, electronic, bonding, magnetic, and optical properties of bimetallic [Cu(n)Ru(m)](+/0/-) (n + m ≤ 3; n, m = 0-3) clusters were computed in the framework of the density functional theory (DFT) and time-dependent DFT (TD-DFT) using the full-range PBE0 nonlocal hybrid GGA functional combined with the Def2-QZVPP basis sets. Several low-lying states have been investigated and the stability of the ground state spinomers was estimated with respect to all possible fragmentation schemes. Molecular orbital and population analysis schemes along with computed electronic parameters illustrated the details of the bonding mechanisms in the [Cu(n Ru(m)](+/0/-) clusters. The TD-DFT computed UV-visible absorption spectra of the bimetallic clusters have been fully analyzed and assignments of all principal electronic transitions were made and interpreted in terms of contribution from specific molecular orbital excitations.     

Nonlinear optical properties of confined excitons in clusters

Size effects in femtosecond photon echo spectroscopy of neat clusters are calculated using a quasiparticle representation of the nonlinear response. We extend our previous study of cooperative effects on the nonlinear response of assemblies of two level molecules [J. A. Leegwater and S. Mukamel, Phys. Rev. A46, 452 (1992)] to allow for nuclear motion and to have an s-p model of polarizable atoms. Photon echos in Benzene/Argon clusters are calculated using a semiclassical phase averaging procedure [L. E. Fried and S. Mukamel, Adv. Chem. Phys. (in Press)].     

Electronic structure calculations of small Al n (n=2–8) clusters

The electronic states of small Al _n (n=2–8) clusters have been calculated with a relativistic ab-initio MO-LCAO Dirac-Fock-Slater method using numerical atomic DFS wave-functions. The excitation energies were obtained from a ground state calculation of neutral clusters, and in addition from negative clusters charged by half an electron in order to account for part of the relaxation. These energies are compared with experimental photo-electron spectra.     

Dimerization of argon and the properties of its small clusters

Statistical thermodynamic means are used to study the bound state of a small cluster A_N (2 ≤ N ≤ 5) of Lennard-Jones particles in a spherical cavity. The statistical sum is calculated by the Monte Carlo method. For the dimer, integration is reduced to quadratures. The integration region contains only phase space points corresponding to the bound cluster state. Dimerization constant 2A = A₂ is calculated via the probability of finding a molecule in the bound state using the example of argon.     

Structure and some properties of small water clusters

The energies and structures of many small water clusters (H₂O)_n (n=8-26) are calculated using the atom-atom potential functions suggested earlier. For each n, several stable configurations were found that differ in the number of H-bonds and in the topology of the graphs formed by such bonds. The clusters in which the molecules lie at the vertices of convex polyhedra have the lowest-energy but other configurations may have close or even lower energies. For the most stable clusters, the energy dependence on n is close to linear. At 300 K, the mean energies of the clusters behave similarly. Monte-Carlo simulations showed that the clusters undergo pseudomelting at approximately 200 K. Puebla Autonomous University, Puebla, Mexico, Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences. Institute of Mathematical Problems of Biology, Russian Academy of Sciences. Institute of Physical Chemistry, Russian Academy of Sciences Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 6 pp. 113–121, November–December, 1994. Translated by L. Smolina     

Calculation of the properties of small boron and aluminum clusters

CNDO calculations were carried out for B _n and Al _n clusters, n=2–7, 12, and 13. The energetically most stable cluster structures were determined for each n. The results show that the stability of the more compact structures increases in going from boron to aluminum. We conclude that the CNDO model used is suitable for discerning the difference in the structure formation of boron and aluminum, which is manifest, in particular, in the formation of crystalline modifications by boron based on an icosahedral structural element, while crystalline aluminum has an FCC lattice.Institute of Theoretical and Applied Mechanics, Siberian Branch, Academy of Sciences of the USSR. Translated from Zhurnal Strukturnoi Khimii, Vol. 30, No. 5, pp. 48–54, September–October, 1989.     

Simulating the optical properties of CdSe clusters using the RT-TDDFT approach

The structural and electronic properties of the CdSe nanoclusters, which have been intended to model quantum dots, have been examined by means of time-dependent density functional (TDDFT) calculations. The optical spectra were first simulated using the standard linear response implementation of the TDDFT (LR-TDDFT) in a series of calculations performed using different basis sets and exchange–correlation functionals. In a second step, the real-time TDDFT implementation (RT-TDDFT) was used to simulate the optical absorption spectra of the CdSe nanoclusters, both naked and capped with ligands. In general, we found that the RT-TDDFT approach successfully reproduced the optical spectrum of CdSe clusters offering a good compromise to render both the optical and the geometrical properties of the CdSe clusters at lower computational costs. While for small systems, the standard TDDFT is better suited, for medium- to large-sized systems, the real-time TDDFT becomes competitive and more efficient.     

Evolution of the properties of Al(n)N(n) clusters with size

A global optimization of stoichiometric (AlN)(n) clusters (n = 1-25, 30, 35, ..., 95, 100) has been performed using the basin-hopping (BH) method and describing the interactions with simple and yet realistic interatomic potentials. The results for the smaller isomers agree with those of previous electronic structure calculations, thus validating the present scheme. The lowest-energy isomers found can be classified in three different categories according to their structural motifs: (i) small clusters (n = 2-5), with planar ring structures and 2-fold coordination, (ii) medium clusters (n = 6-40), where a competition between stacked rings and globular-like empty cages exists, and (iii) large clusters (n > 40), large enough to mix different elements of the previous stage. All the atoms in small and medium-sized clusters are in the surface, while large clusters start to display interior atoms. Large clusters display a competition between tetrahedral and octahedral-like features: the former lead to a lower energy interior in the cluster, while the latter allow for surface terminations with a lower energy. All of the properties studied present different regimes according to the above classification. It is of particular interest that the local properties of the interior atoms do converge to the bulk limit. The isomers with n = 6 and 12 are specially stable with respect to the gain or loss of AlN molecules.     

The optical absorption spectra of small Silver clusters (n=8–39) embedded in rare gas matrices

The optical absorption of small mass selected Ag_n-clusters (n=8–39) embedded in solid Ar, Kr and Xe has been measured. Strong absorption has been found between 3 and 4.5 eV. The absorption spectra show 1 to 3 major peaks depending on the cluster size. The width of these peaks is smaller than in gas phase photodepletion experiments of silver ions, most likely due to the low and well defined temperature of the clusters in the matrix. The results are compared to a simple model based on a Drude metal, taking into account the spillout of the electrons and allowing for a deviation of the cluster from a spherical shape. Absorption cross sections scale with the number of valence electrons.     

Evolution of superhalogen properties in PtCl(n) clusters

We have systematically calculated the ground state geometries, relative stability, electronic structure, and spectroscopic properties of PtCl(n) (n = 1-7) clusters. The bonding in these clusters is dominated by covalent interaction. In neutral clusters, chlorine atoms are chemically bound to Pt up to n = 5. However, in neutral PtCl(6) and PtCl(7) clusters, two of the chlorine atoms bind molecularly while the remaining bind as individual atoms. In the negative ions, this happens only in the case of PtCl(7) cluster. The geometries of both neutral and anionic clusters can be considered as fragments of an octahedron and are attributed to the stabilization associated with splitting of partially filled d orbitals under the chloride ligand field. The electron affinity of PtCl(n) clusters rises steadily with n, reaching a maximum value of 5.81 eV in PtCl(5). PtCl(n) clusters with n ≥ 3 are all superhalogens with electron affinities larger than that of chlorine. The accuracy of our results has been verified by carrying out photoelectron spectroscopy experiments on PtCl(n)(-) anion clusters.