Second Energy Difference Research Articles

Structures and stability of B-doped Al clusters: AlnB and AlnB2 (n=1–7)

Various structural possibilities for Al(n)B(m) (n=1-7, m=1-2) neutral isomers were investigated using B3LYP6-311G(d) and CCSD(T)6-311G(d) methods. Our calculations predicted the existence of a number of previously unknown isomers. The B atom favors to locate over/inside of all clusters in this series. All structures of the Al(n)B (n=2-7) may be derived from capping/putting a B atom over/inside the Al(n) cluster. All Al(n)B(2) (n=1-5) may be understood as two substitutions of Al atoms by B atoms in the Al(n+2) molecule. The strong B-B bond is a dominant factor in the building-up principle of mixed Al(n)B(2) neutral clusters. The second difference in energy showed that the Al(n)B(m) clusters with even n+m are more stable than those with odd n+m. Our results and analyses revealed that the mixed Al-B clusters exhibit aromatic behaviors.

Density functional study of structural and electronic properties of AlnN (1 ≤ n ≤ 12) clusters

AbstractLow‐lying equilibrium geometric structures of AlnN (n = 1–12) clusters obtained by an all‐electron linear combination of atomic orbital approach, within spin‐polarized density functional theory, are reported. The binding energy, dissociation energy, and stability of these clusters are studied within the local spin density approximation (LSDA) and the three‐parameter hybrid generalized gradient approximation (GGA) due to Becke–Lee–Yang–Parr (B3LYP). Ionization potentials, electron affinities, hardness, and static dipole polarizabilities are calculated for the ground‐state structures within the GGA. It is observed that symmetric structures with the nitrogen atom occupying the internal position are lowest‐energy geometries. Generalized gradient approximation extends bond lengths as compared with the LSDA lengths. The odd–even oscillations in the dissociation energy, the second differences in energy, the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps, the ionization potential, the electron affinity, and the hardness are more pronounced within the GGA. The stability analysis based on the energies clearly shows the Al7N cluster to be endowed with special stability. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

Structural and electronic properties of Si n, Si n+, and AlSi n-1 (n=2-13) clusters: theoretical investigation based on ab initio molecular orbital theory.

The geometric and electronic structures of Si(n), Si(n) (+), and AlSi(n-1) clusters (2< or =n< or =13) have been investigated using the ab initio molecular orbital theory under the density functional theory formalism. The hybrid exchange-correlation energy function (B3LYP) and a standard split-valence basis set with polarization functions [6-31G(d)] were employed for this purpose. Relative stabilities of these clusters have been analyzed based on their binding energies, second difference in energy (Delta (2)E) and fragmentation behavior. The equilibrium geometry of the neutral and charged Si(n) clusters show similar structural growth. However, significant differences have been observed in the electronic structure leading to their different stability pattern. While for neutral clusters, the Si(10) is magic, the extra stability of the Si(11) (+) cluster over the Si(10) (+) and Si(12) (+) bears evidence for the magic behavior of the Si(11) (+) cluster, which is in excellent agreement with the recent experimental observations. Similarly for AlSi(n-1) clusters, which is isoelectronic with Si(n) (+) clusters show extra stability of the AlSi(10) cluster suggesting the influence of the electronic structures for different stabilities between neutral and charged clusters. The ground state geometries of the AlSi(n-1) clusters show that the impurity Al atom prefers to substitute for the Si atom, that has the highest coordination number in the host Si(n) cluster. The fragmentation behavior of all these clusters show that while small clusters prefers to evaporate monomer, the larger ones dissociate into two stable clusters of smaller size.

Theoretical study of structures and stabilities of C mN 2 ( m=1–14) ions

Geometrical and electronic properties of C m N 2 ( m=1–14) positively and negatively charged clusters have been investigated by hybrid B3LYP functional at the respective 6-311G(d) and 6-311+G(d) levels. Our results revealed that C m N 2 ( m=2–14) cationic ions and C m N 2 ( m=6–14) anions form linear conformer with D ∞h symmetry except for C 11N 2 + cationic ion whereas C m N 2 ( m=1–5) anions form chain-like arrangements. Two N atoms favor to bond at ends in linear and chain-like configurations. Both calculated HOMO–LUMO gaps and adiabatic ionization potentials showed that the C m N 2 ( m=1–14) clusters with even m are more stable than those with odd m. The second difference in energy for C m N 2 + ( m=1–14) ions revealed that the cationic ions with even m are more stable than those with odd m, which is consistent with the observed cationic even–odd alternation of the TOF signal intensities. The relative stability of anions is in opposition to that of cationic clusters.

Density-functional investigation of the size dependence of the electronic structure of mixed aluminum-sodium clusters

Equilibrium geometries and electronic-structure properties have been obtained for cationic, anionic, and neutral ${\mathrm{Al}}_{n}\mathrm{Na}$ and ${\mathrm{Al}}_{n}{\mathrm{Na}}_{2}$ $(n=1--12)$ clusters within the density-functional theory using the generalized gradient approximation for the exchange-correlation potential. The resulting geometries show that the sodium atom prefers to be on the periphery and does not get trapped. The stability has been investigated by analyzing the binding energy, the dissociation energy, and the second difference in energy. The results indicate that for neutral clusters, ${\mathrm{Al}}_{4}\mathrm{Na}$ and ${\mathrm{Al}}_{7}\mathrm{Na}$ are stable. Considerable enhanced stability is also seen for ${\mathrm{Al}}_{4}{\mathrm{Na}}_{2},$ ${\mathrm{Al}}_{6}{\mathrm{Na}}_{2},$ ${\mathrm{Al}}_{4}{\mathrm{Na}}^{\ensuremath{-}},$ and ${\mathrm{Al}}_{6}{\mathrm{Na}}^{\ensuremath{-}}$ clusters. The stability of these clusters cannot be explained on the basis of a simple jellium model. The calculated vertical ionization potentials are in good agreement with their experimental counterparts. No consistent signature of a monovalent nature for Al is observed in these systems. The addition of sodium atoms is found to quench the weak magnetic moment of pure Al clusters and all ${\mathrm{Al}}_{n}{\mathrm{Na}}_{2}$ clusters are found to be nonmagnetic.

Density functional study of structural and electronic properties of NanMg (1⩽n⩽12) clusters

Low-lying equilibrium geometric structures of NanMg (n=1–12) clusters obtained by an all-electron linear combination of atomic orbital approach, within spin-polarized density functional theory, are reported. The binding energy, dissociation energy, and stability of these clusters are studied within the local spin density approximation (LSDA) and the three-parameter hybrid generalized gradient approximation (GGA) due to Becke-Lee-Yang-Parr (B3LYP). Ionization potentials, electron affinities, hardness, and static dipole polarizabilities are calculated for the ground-state structures within the GGA. It is observed that for clusters with n&amp;lt;9, symmetric structures with the magnesium atom occupying the internal position are higher in energy (typically by less than 1 eV) than those where Mg occupies a peripheral position. It is found that the relative ordering of the isomers is influenced by the nonlocal exchange-correlation effects for small clusters. Generalized gradient approximation extends bond lengths and widens the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), as compared to the LSDA gap. The odd-even oscillations in the dissociation energy, the second differences in energy, the HOMO–LUMO gaps, the ionization potential, the electron affinity, and the hardness are more pronounced within the GGA. The stability analysis based on the energetics clearly shows the Na6Mg cluster to be endowed with special stability, which occurs because of an electronic shell closure.

Ground-state geometries and stability of Na $\mathsf{_n}$ Mg $\mathsf{(n=1\mbox{--}12)}$ clusters using ab initio molecular dynamics method

The ground-state geometries, energetics and the stability of ( n =1-12) clusters are studied using ab initio molecular dynamics method. Our results indicate that the ground-state geometries of large clusters ( ) are different from those of clusters where a trivalent impurity Al is added to the same monovalent host Na. Other features observed are an early appearance of 3-dimensional structure and a pentagonal growth path from n =6 up to n =11. As expected, the ground-state geometry of is not an icosahedron but can be viewed as a distorted form of one of the low lying geometries of cluster. In the energetically favored structures impurity atom Mg is never located at the center of the cluster. The stability analysis based on the energetics shows (8 valence electrons) to be the most stable. In addition there is a remarkable even-odd pattern observed in the dissociation energy and the second difference in energy which is absent in earlier studies of and clusters.