Size- and shape-dependent polarizabilities of sandwich and rice-ball Co(n)Bz(m) clusters from density functional theory

The dipole polarizabilities of Co(n)Bz(m), (n, m = 1-4, m = n, n + 1) clusters are studied by means of an all-electron gradient-corrected density functional theory and finite field method. The dipole moments are relatively large for most of the clusters, implying their asymmetric structures. The total polarizability increases rapidly as cluster size, whereas the average polarizability shows "odd-even" oscillation with relatively large values at (n, n + 1). The polarizabilities exhibit clear shape-dependent variation, and the sandwich structures have systematically larger polarizability and anisotropy than the rice-ball isomers. The dipole polarizabilities are further analyzed in terms of the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap, ionization potential, and electron delocalization volume. We conclude that the polarizability variations are determined by the interplay between the geometrical and electronic properties of the clusters.     

Geometrical Structures and Electronic Properties of Copper-Doped Aluminum Clusters

Using density function theory (DFT), the Cu-doped Aln (n=1?15) clusters have been stud-ied. The electron a±nity, ionization potential, Mulliken population analysis of Cu, mean polarizability, polarizability anisotropy, dipole moments and HOMO-LUMO gaps have also been calculated on the basis of optimized geometries. The results indicate that there is magic numbers in copper-doped aluminum clusters and electronic characteristic depended on the size of clusters. As n=13, the electron affinity and ionization potential of cluster changed more than 0.3 and 0.6 eV respectively, compared with neighborhood clusters.     

The effect of geometry on cluster polarizability: studies of sodium, copper, and silicon clusters at shape-transition sizes

The electronic properties of Na(16), Cu(16,) and Si(20-28) clusters were calculated using density functional theory with the generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof. These clusters are special, as transitions in cluster shape occur at these sizes in the Na(n), Cu(n), and Si(n) cluster systems, respectively. Low-energy isomers that are comparable in stability, but possess distinctly different shapes, exist at each of these sizes, making these sets of isomers useful as probes of geometrical effects on cluster properties. Results for ionization potentials, electron affinities, and polarizabilities are shown to have a characteristic dependence on cluster shape. An analysis of the results reveals a close relationship between polarizability and cluster volume for all the isomers studied, despite the differences in cluster type and geometry. This relationship accounts for variations in polarizabilities among isomers of the same size, but different shapes, whereas previously published rules relating the polarizability to other cluster properties do not.     

Ab initio studies of properties of small potassium clusters

We have studied the properties of various isomers of potassium clusters containing even number of atoms ranging from 2 to 20 at the ab initio level. The geometry optimization calculations of the isomers of each cluster are performed by using all-electron density functional theory with gradient corrected exchange-correlation functional. Using the optimized geometries of different isomers we investigate the evolution of binding energy, ionization potential, and static polarizability with the increasing size of the clusters. The polarizabilities are calculated by employing M?ller-Plesset perturbation theory and time-dependent density functional theory. The polarizabilities of dimer and tetramer are also calculated by employing large basis set coupled cluster theory with single and double excitations and perturbative triple excitations. The time-dependent density functional theory calculations of polarizabilities are carried out with two different exchange-correlation potentials: (i) an asymptotically correct model potential and (ii) within the local density approximation. A systematic comparison with the other available theoretical and experimental data for various properties of small potassium clusters mentioned above has been performed. These comparisons reveal that both the binding energy and the ionization potential obtained with gradient-corrected potential match quite well with the already published data. Similarly, the polarizabilities obtained with M?ller-Plesset perturbation theory and with model potential are quite close to each other and also close to experimental data.     

New insights into applicability of electron-counting rules in transition metal encapsulating Ge cage clusters

The relative stability of Sc, Ti, and V encapsulating Ge(n) clusters in the size range n = 14-20 has been studied through first-principles electronic structure calculations based on density functional theory. Variations of the embedding energy, gap between the highest occupied and the lowest occupied molecular orbitals, ionization potential, vertical detachment energy, and electron affinity with cluster size have been calculated to identify clusters with enhanced stability. The enhanced stability of some clusters can be very well explained as due to the formation of a filled shell free-electron gas inside the Ge cages. For the first time, direct evidence of the formation of a free-electron gas is also presented. In some other clusters, enhanced stability is found to originate from geometric effects. Some clusters that may be expected to have enhanced stability from simple electron counting rules do not show that. These results provide new insights into the long-standing question of whether electron counting rules can explain the relative stability of transition metal encapsulated semiconductor clusters and show that these clusters are too complex for such simple generalizations.     

Al7Ag and Al7Au clusters with large highest occupied molecular orbital-lowest unoccupied molecular orbital gap

The candidate structures for the ground-state geometry of the Al(7)M (M = Li, Cu, Ag, and Au) clusters are obtained within the spin-polarized density functional theory. Absorption energy, vertical ionization potential, vertical electron affinity, and the energy gap between the highest occupied molecular orbital (HOMO) level and the lowest unoccupied molecular orbital (LUMO) level have been calculated to investigate the effects of doping. Doping with Ag or Au can lead to a large HOMO-LUMO gap, low electron affinity, and increased ionization potential of Al(7) cluster. In the lowest-energy structure of the Al(7)Au cluster, the Al atom binding to the Al(6)Au acts monovalent and the other six Al atoms are trivalent. Thus, the Al(7)Au cluster has 20 valence electrons, and its enhanced stability may be due to the electronic shell closure effect.     

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

Low‐lying equilibrium geometric structures of Al_nN (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     

Electronic and optical properties of edge modified peritetracene: a DFT study

Peritetracene (PTA) molecules have promising applications in organic electronics and organic light-emitting diodes, but the major constraints come from their poor stability with higher energy gap. We have investigated the stability, electronic, and optical properties of different electron-donating- and electron-withdrawing-substituted PTA molecule groups using density functional theory (DFT) and time-dependent density functional theory (TDDFT) methods. On substituting suitable electron donor and acceptor groups, the energy gap of PTA molecules reduces up to 0.37 eV with an increase in their stability. The stabilities of considered PTA molecules have been investigated using the distribution pattern of frontier molecular orbital energies. The charge transfer properties with smaller ionization potential and larger electron affinity for PTA molecule have been evaluated using Koopmans’ theorem. Enhancement in dipole moment, polarizability, and hyperpolarizability of PTA substituted with electron-donating groups shows the presence of NLO properties. Also, we have investigated the spectroscopic properties of different electron-donating- and electron-withdrawing-substituted PTA molecule groups. Our spectroscopic properties show the bathochromic shift and small hypsochromic shifts in wavelengths of PTA with substituents groups. It is therefore concluded that the –NCH₃ and –NO₂ substituent groups on PTA are observed to have the strongest and highest stability than the other substituent groups considered.

     

Structures and electronic properties of germanium-doped Ni<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> clusters, <Emphasis Type="Italic">n</Emphasis> = 13–23

The magnetic property and electronic properties such as binding energy, charge transfer, ionization potential and electron affinity of the Ni _n–1Ge (n = 13–23) neutral and ionic clusters have been studied using the density functional theory calculations with the PBE exchange-correlation energy functional. The calculated total magnetic moments decrease with the addition of Ge atom. Both the calculated ionization potential and electron affinity exhibit an oscillating behavior as the cluster size increases.     

The structural and electronic properties of In(n)N(n = 1-13) clusters

The structural and electronic properties of In(n)N(n=1-13) clusters have been investigated by density-functional theory with the generalized gradient approximation. The results indicate that the equilibrium structures of In(n)N are linear for n=1,2, planar for n=3-5, and three dimensional for n=6-13. Maximum peaks were observed for In(n)N clusters at n=3,7,9 on the size dependence for second-order energy difference. These imply that these clusters possess relatively higher stability, which is consistent with the case of binding energy per atom. Moreover, the results show that the bonding in small In(n)N clusters has a little ionic character by Mulliken population analysis. The energy gap between the highest occupied and lowest unoccupied molecular orbitals, the vertical ionization potential and electron vertical affinity (VIP and VEA) form an even-odd alternating pattern with increasing cluster size. In general, the VIP tends to lower as the cluster size increases, while the VEA tends to increase as the cluster size increases.     

Density functional studies of LiN and LiN+ (N = 2–30) clusters: Structure,binding and charge distribution

Density functional calculations using B3LYP/6‐311G method have been carried out for small to medium‐sized lithium clusters (Li_N, N = 2–30). The optimized geometries of neutral and singly charged clusters, their binding energies, ionization potential, electron affinity, chemical potential, softness, hardness, highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO–LUMO) gap, and static dipole polarizability have been investigated systematically. In addition, we study the distribution of partial charges in detail using natural population analysis (NPA) in small‐sized clusters (Li_N, N = 2–10), both neutral and cationic, and demonstrate the correlation between symmetry and charge. Uniform distribution of charges in cationic clusters confirms them to be energetically more favorable than the neutral counterparts. Whenever possible, results have been compared with available data. An excellent agreement in every case supports new results as reliable predictions. A careful study of optimized geometries shows that Li₉ is derivable from bulk Li structure, i.e., body centered cubic cell, and higher clusters have optimized shapes derived from this. Further, the turnover form two to three dimensional structure occurs at cluster size N = 6. The quantity α^1/3 (α = polarizability) per atom is found to be broadly proportional to softness (per atom) as well as inverse ionization potential (per atom). The present work forms a sound basis for further study of large‐sized clusters as well as other atomic clusters. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

The calculation of molar polarizabilities by the CNDO/2 method: Correlation with the hydrophobic parameter,log P

Results of molecular orbital (MO) calculations by the complete neglect of differential overlap (CNDO /2) method on 50 small molecules are reported. The summation of calculated atomic polarizabilities are equated with molecular polarizabilities, and these are compared with experimentally determined values. It is found that there is very good agreement between calculated and experimental molecular polarizability. This provides a reliable method for the determination of molecular polarizabilities for compounds for which experimental values are not known. The relationship between log P and polarizability is discussed and analyzed in terms of contributions from electronic components to the partitioning energy.     

Atomic and electronic structures of neutral and charged Pbn clusters (n=2-15): theoretical investigation based on density functional theory

The geometric and electronic structures of the Pbn+ clusters (n=2-15) have been investigated and compared with neutral clusters. The search for several low-lying isomers was carried out under the framework of the density functional theory formalism using the generalized gradient approximation for the exchange correlation energy. The wave functions were expanded using a plane wave basis set and the electron-ion interactions have been described by the projector augmented wave method. The ground state geometries of the singly positively charged Pbn+ clusters showed compact growth pattern as those observed for neutrals with small local distortions. Based on the total energy of the lowest energy isomers, a systematic analysis was carried out to obtain the physicochemical properties, viz., binding energy, second order difference in energy, and fragmentation behavior. It is found that n=4, 7, 10, and 13 clusters are more stable than their neighbors, reflecting good agreement with experimental observation. The chemical stability of these clusters was analyzed by evaluating their energy gap between the highest occupied and lowest unoccupied molecular orbitals and adiabatic ionization potentials. The results revealed that, although Pb13 showed higher stability from the total energy analysis, its energy gap and ionization potential do not follow the trend. Albeit of higher stability in terms of binding energy, the lower ionization potential of Pb13 is interesting which has been explained based on its electronic structure through the density of states and electron shell filling model of spherical clusters.     

Between geometry, stability, and polarizability: density functional theory studies of silicon clusters Sin (n = 3-10)

The relationship between the polarizability, stability, and the geometry of small-size silicon clusters has been investigated by the density functional theory methods. Results obtained at local density approximation/Vosko-Wilk-Nusair and general gradient approximation/BLYP levels with polarized even-tempered basis set of quadruple zeta quality are presented and compared with those obtained by the B3LYP method, as well as with the ab initio results in recent literature. We have found that the polarizability is directly related to the size of the energy gap between symmetry-compatible bonding and antibonding molecular orbitals, but not necessarily to the size of the HOMO-LUMO (highest occupied molecular orbital-lowest unoccupied molecular orbital) gap. Furthermore, we have defined two structural parameters, namely, the averaged Si-Si distances and the standard deviation of the Si-Si distances, which were found to correlate remarkably well with the binding energy of the clusters and the HOMO-LUMO gap, respectively. These straightforward correlations would, therefore, provide a means to predict the physical properties, in particular, the polarizability and the stability, simply based on the structural information of the cluster.     

Structural and electronic properties of neutral and ionic Ga(n)On clusters with n = 4-7

We report the results of a theoretical study of neutral, anionic, and cationic Ga(n)On clusters (n = 4-7), focusing on their ground-state configurations, stability, and electronic properties. The structural motif of these small gallium oxide clusters appears to be a rhombus or a hexagonal ring with alternate gallium and oxygen atoms. With the increase in the cluster size from Ga4O4 to Ga7O7, the ground-state configurations show a transition from planar to quasi-planar to three-dimensional structure that maximizes the number of ionic metal-oxygen bonds in the cluster. The ionization-induced distortions in the ground state of the respective neutral clusters are small. However, the nature of the LUMO orbital of the neutral isomers is found to be a key factor in determining the ordering of the low-lying isomers of the corresponding anionic clusters. A sequential addition of a GaO unit to the GaO monomer initially increases the binding energy, though values of the ionization potential and the electron affinity do not show any systematic variation in these clusters.     

Ab initio studies on the electronic structure and properties of aluminum hydrides that are analogues of boron hydrides

Although the boron hydrides are well-known in the literature, the aluminum hydride chemistry is limited to very few systems such as AlH(3), its dimer, and its polymeric form. In view of the recent experimental studies on the possible existence of the aluminum hydrides, herein, we have undertaken a systematic study on the electronic structure and properties of these aluminum hydrides. Under this, we have studied different classes of hydrides, viz., closo (Al(n)H(n+2)), nido (Al(n)H(n+4)), and arachno (Al(n)H(n+6)), similar to the boranes. All the aluminum hydrides are found to have exceptionally large highest-occupied molecular orbital-lowest-unoccupied molecular orbital gaps, low electron affinities, large ionization potentials and also large enthalpy and free energy of atomization. In addition, most of the structures are also found to have high symmetries. These exceptional properties can be indicative of the pronounced stability, and hence, it is expected that other aluminum hydride complexes can indeed be observed experimentally.