Odd Alternation Research Articles

Theoretical investigation on structural evolution, energetic stability trend and electronic properties of Au n Cd(n=1–12)

We systematically studied the geometrical structures, relative stabilities, electronic properties and chemical hardness of Au n Cd (n =1–12) clusters based on the framework of the density functional theory using relativistic all-electron methods. Low-lying energy structures include two-dimensional and three-dimensional geometries. Especially, all the lowest-energy structures of Au n Cd (n =1 −12) clusters are inclined to be planar geometries with slight distortion, in which the dopant Cd atom has higher coordination at n =2–6, but lower coordination at n =7–12. The fragmentation energies, second-order difference of energies, the highest occupied–lowest unoccupied molecular orbital gaps and chemical hardness of Au n Cd and Au n+1 exhibit a pronounced even–odd alternations phenomenon in the reverse order This result indicates that the geometrical, electronic and chemical stabilities of Au n Cd with even number of valence electrons are higher than those of the neighbouring Au n Cd with odd number of valence electrons and corresponding Au n+1 with odd number of valence electrons. Additionally, 4d valence electrons orbital of impurity Cd atom in Au n Cd hardly joins in the orbital interactions compared with 5d valence electrons of corresponding Au atom in Au n+1. Au–Cd bonds of Au n Cd clusters are weaker and have more obviously ionic-like characteristics than the corresponding Au–Au bonds of Au n+1. The impurity Cd atom can change the chemical stability pattern of pure gold clusters, namely the even-numbered Au n Cd are less reactive than the corresponding Au n+1 and neighbouring odd-numbered Au n Cd.

Small Cu Clusters Adsorbed on ZnO(101̅0) Show Even–Odd Alternations in Stability and Charge Transfer

Using hybrid density functional theory, we investigate structural and electronic properties of small Cun clusters (with n ≤ 9) adsorbed on the nonpolar ZnO(101̅0) surface. The Cu clusters grow in a planar fashion up to a size of six atoms, after which the clusters take on a polyhedral shape. We find even–odd alternations with respect to both cluster stability (for n = 1–6) and cluster charge, as a function of the number of atoms. Even-numbered clusters are always charge-neutral, while odd-numbered clusters can become positively charged by donation of an electron to the ZnO conduction band, which can be traced back to the fact that the ionization energies of odd-numbered gas-phase Cu clusters are lower than for even-numbered ones. The most stable adsorbed odd-numbered clusters are neutral and planar for n ≤ 3 and positively charged and polyhedral for n ≥ 7. For n = 5, both neutral planar and positively charged polyhedral configurations are similarly stable.

DFT and QTAIM studies on structure and stability of beryllium doped gold clusters

Impurity-doped clusters particularly the gold doped bimetallic clusters have received considerable attention in the last few years. The doped atoms can considerably alter the geometrical and electronic properties as well as the stability of gold clusters. Density functional theory (DFT) with B3LYP functional have been applied to study the geometrical structures and relative stabilities of small bimetallic neutral, cationic and anionic AunBe (n=1–6) and AunBe2 (n=1–5) clusters. For AunBe2 clusters, we obtained only planar structure whereas AunBe clusters show both planar and three dimensional structures. The relative stabilities of the clusters are compared on the basis of average binding energies, fragmentation energies and second order difference of energies. The fragmentation energies and second order difference of energies of all the three types of clusters shows the even–odd alternation phenomenon. The nature of bonding interaction is also investigated by using Bader’s quantum theory of atoms in molecules (QTAIM). Based on QTAIM results, we can suggest that the beryllium doped clusters are more stable than the pure gold clusters due to strong covalent interaction between the gold and beryllium metal centres.

First-principles study on stability and photoelectron spectroscopy of GanAs2(n = 1–9) clusters

The stability and photoelectron spectroscopy of the GanAs2(n=1–9) clusters have been studied by using first-principles based on density functional theory (DFT). Our calculations reveal that the stabilities of the GanAs2(n=1–9) clusters tend to increase with the increase of the number of total atoms. The calculated second-order difference values of the binding energy show a certain law of even–odd alternation, and the value of the even-numbered clusters is much larger than those of the odd-numbered ones. The energy gap Egap also shows a certain law of even–odd alternation, i.e. the Egap of the even-numbered clusters is much larger than the odd-numbered ones. The Egap of the clusters is between 0.2eV and 0.6eV, it will provide a reference for GaAs defect level research. The GanAs2(n=1–9) clusters are potential to detect and emit THz radiation due to their ground-state vibration frequency are in THz range.

DFT study of size-dependent geometries, stabilities and electronic properties of Si2Agn clusters: comparison with pure silver clusters

The equilibrium geometric structures, stabilities and electronic properties of Si2Agn (n = 1–8) and pure silver Agn (n ≤ 10) clusters have been systematically investigated by using meta-generalised gradient approximation. Due to sp3 hybridisation, the lowest energy structures of Si2Agn clusters for n > 2 favour the three-dimensional structure. The silicon atoms prefer to be located at the surface of the host silver clusters. By analysing the relative stabilities, it is found that the di-bridged structure Si2Ag2 isomer is the most stable structure for Si2Agn (n = 1–8) clusters. The highest occupied–lowest unoccupied molecular orbital gaps, exhibiting a pronounced even–odd alternation, indicate that the doped clusters with even number of atoms have enhanced chemical stability than those with odd number of atoms. The results of Wiberg bond indices and electronic localisation function show that the stronger Si–Si and Si–Ag interaction may be the main driving force for the higher stability of Si2Agn clusters.

Au-doped carbon clusters AuC n with n = 1–11: a theoretical investigation

The hybrid HF/DFT method B3LYP has been employed to investigate the geometrical and electronic structures of AuCn (n = 1–11) clusters. The properties such as geometrical parameters and electronic energies are determined for open-chain and cyclic species. Our results indicate that the open-chain structures with low spin states (doublet) are more stable than the cyclic ones for the small sizes clusters (n ≤ 9), as the cluster sizes increase (n = 10, 11), the cyclic species are more stable. The incremental binding energies show a smooth even–odd alternation phenomenon for open-chain species, n-even (n is the numbers of C atom in the clusters) species have the stronger stabilities relative to the adjacent odd-numbered ones. In addition, the most favorable dissociation channels are determined by calculating the fragmentation energies accompanying various possible pathways. The studied clusters incline to be dissociated to Au + Cn and AuCn−3 + C3 fragments.

Properties of fast carbon cluster microbeams produced with a tapered capillary

We study the transmission properties of fast cluster ions (Cn+ (n=2–4) with velocities ranging from 0.89 to 1.79a.u.) through a single tapered capillary with an outlet diameter of 13.7μm. We investigate the projectile-velocity dependence of the transmission fraction from the measurements of transmitted particle energy spectra. It is found that the non-fragmentation fraction of C2+ projectiles increases with decreasing velocity, indicating that fragmentation occurs mainly via close collisions with the surfaces of the capillary wall. For Cn+ (n=2–4) ions with the same incident velocity, the cluster-size dependence of the non-fragmentation fraction shows even–odd alternation, implying that the fraction includes contributions from stable clusters surviving the grazing scattering process at the capillary surface. We also find that the angular distribution of transmitted particles is narrower for cluster projectiles compared with atomic projectiles.

Structures and stabilities of GaCn (n = 1–10) clusters

A theoretical study of the small Gallium-doped carbon clusters GaCn (n=1–10) has been studied with density functional theory (DFT) method at the B3LYP/6-311+G* level. The computed properties include equilibrium geometries, electronic energies, vibrational frequencies, dipole moments, and rotational constants for individual species. According to these calculations, except for smaller GaC2, the open-chain linear or quasi-linear isomers with the Gallium atom bound to the end of the carbon chain are the most stable geometry in all cases. The electronic ground state is found to be a doublet state for the GaCn clusters, with the only exception of the smallest GaC. The incremental binding energy diagram shows a strong even–odd alternation in the cluster stability for these linear GaCn, with their n-even members being much more stable than the adjacent odd-numbered ones. These parity effects also appear in the second difference in energy curves. In addition, by comparing with the fragmentation energies accompanying various channels, the most favorable dissociation channels are acquired.

Density-functional investigation of the geometries, stabilities, electronic, and magnetic properties of gold cluster anions doped with aluminum: [formula omitted] (1 ⩽ n ⩽ 8)

The geometrical structures, relative stabilities, electronic and magnetic properties of the AunAl- (1⩽n⩽8) clusters are systematically investigated by the first-principles density functional calculations at the PW91PW91 level. The results show that doping with a single Al atom can dramatically affect the ground-state geometries of the Aun+1- clusters. The calculated fragmentation energy, second-order difference of the total energies and the highest occupied-lowest unoccupied molecular orbital (HOMO–LUMO) energy gaps exhibit an interesting, oscillatory behavior as a function of the cluster size. Furthermore, both the total and local magnetic moments display an obvious even–odd alternation phenomenon with the number of gold atoms.

Density-functional theory study of the geometries, stabilities, and electronic properties of Au n Rb (n = 1–10) clusters: comparison with pure gold clusters

The density functional method with the relativistic effective core potential has been employed to investigate systematically the geometric structures, relative stabilities, growth-pattern behavior, and electronic properties of small bimetallic Au n Rb (n = 1–10) and pure gold Au n (n ≤ 11) clusters. For the geometric structures of the Au n Rb (n = 1–10) clusters, the dominant growth pattern is for a Rb-substituted Au n +1 cluster or one Au atom capped on a Au n –1Rb cluster, and the turnover point from a two-dimensional to a three-dimensional structure occurs at n = 4. Moreover, the stability of the ground-state structures of these clusters has been examined via an analysis of the average atomic binding energies, fragmentation energies, and the second-order difference of energies as a function of cluster size. The results exhibit a pronounced even–odd alternation phenomenon. The same pronounced even–odd alternations are found for the HOMO–LUMO gap, VIPs, VEAs, and the chemical hardness. In addition, about one electron charge transfers from the Au n host to the Rb atom in each corresponding Au n Rb cluster.

Competition between monomer and dimer fragmentation pathways of cationic CuN clusters of N = 2–20

Density functional theory calculations are performed to study the structural evolution of cationic copper clusters of N = 2–20 size range. The first shape transition occurs at N = 4, from planar to three dimensional, while the second at N = 16, from layered to capped icosahedra. Distinct even–odd alternation and closing-shell effects in binding energy are noted when size varies. Two fragmentation pathways for each cation are investigated and compared to available experiments. The competition between the two pathways is rationalized from respective dissociation energies which are size and structure dependent.

A theoretical study of the dependence of the ASxSi6−x cluster structures and properties on composition

The effect of the composition ratio between arsenic and silicon atoms on the structures and properties of AsxSi6−x (x = 0–6) have been systematically investigated using the density functional theory at the B3LYP/6-311+G* level. The AsxSi6−x clusters prefer substitutional rather than attaching structures; the Si-rich clusters favor Si6-like structures, whereas the As-rich clusters prefer As6-like structures. The As atoms locating at the framework may explain the difficulty of removal of arsenic impurities from polycrystalline silicon. In general, the average binding energies gradually decrease, implying the AsxSi6−x clusters become increasingly unstable as x increases. Both the HOMO-LUMO gaps and the As-dissociation energies present a strong even–odd alternation, implying alternating chemical stability, with the even x members being more stable than the odd ones. The dissociation energies of an As atom from AsxSi6−x are: 3.07, 2.84, 1.84, 2.52, 1.86, and 2.85 eV, for x = 1–6, respectively, and 3.80, 3.08, 2.64, 3.01, 2.93, 3.16 eV for Si (x = 0–5). These dissociation energy results should provide a useful reference for further experimental investigations. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

Density functional study of the structural and electronic properties of tetra-aluminum oxide (3 ≤ n ≤ 8, λ = 0, −1) clusters

The geometric structures, relative stabilities, and electronic properties of a series of tetra-aluminum oxide clusters, (, ), were systematically investigated using density functional theory calculations at the B3LYP level. The optimized geometries reveal a structural transition from a two-dimensional to a three-dimensional structure for n ≤5 for the neutral species, but the three-dimensional structures are preferable for all negative clusters with the exception of . The dissociation energy, the second difference energy and the highest occupied–lowest unoccupied molecular orbital gaps as a function of the cluster size exhibit a significant even–odd alternation phenomenon. It is found that the neutral cluster is relatively stable and exhibits strong chemical stability. Furthermore, the calculated (vertical and adiabatic) electron detachment energies are also compared with previous experimental data obtained from photoelectron spectra.

Structural, electronic and magnetic properties of gold cluster doped with calcium: Au n Ca (n = 1–8)

The geometrical structures, relative stabilities, electronic and magnetic properties of calcium-doped gold clusters Au n Ca (n = 1–8) have been systematically investigated by employing density functional method at the BP86 level. The optimised geometries show that the ground-state structures are planar structures for Au n Ca (n = 3–8) clusters. Ca-substituted Au n +1 clusters, as well as Au-capped Au n −1Ca clusters, are dominant growth patterns for the Au n Ca clusters. The relative stabilities of Au n Ca clusters for the ground-state structures are analysed based on the averaged binding energies, fragmentation energies and second-order difference of energies. The calculated results reveal that the Au2Ca isomer is the most stable structure for small size Au n Ca (n = 1–8) clusters. The HOMO-LUMO energy gaps as a function of the cluster size exhibit a pronounced even–odd alternation phenomenon. Subsequently, charge transfers and magnetic moment of Au n Ca (n = 1–8) clusters have been analysed further.

Equilibrium Geometries, Stabilities, and Electronic Properties of the Bimetallic M2-doped Aun (M = Ag, Cu; n = 1−10) Clusters: Comparison with Pure Gold Clusters

The density functional method with relativistic effective core potential has been employed to investigate systematically the geometrical structures, relative stabilities, growth-pattern behaviors, and electronic properties of small bimetallic M(2)Au(n) (M = Ag, Cu; n = 1-10) and pure gold Au(n) (n ≤ 12) clusters. The optimized geometries reveal that M(2) substituted Au(n+2) clusters and one Au atom capped M(2)Au(n-1) structures are dominant growth patterns of the stable alloyed M(2)Au(n) clusters. The calculated averaged atomic binding energies, fragmentation energies, and the second-order difference of energies as a function of the cluster size exhibit a pronounced even-odd alternation phenomenon. The analytic results exhibit that the planar structure Ag(2)Au(4) and Cu(2)Au(2) isomers are the most stable geometries of Ag(2)Au(n) and Cu(2)Au(n) clusters, respectively. In addition, the HOMO-LUMO gaps, charge transfers, chemical hardnesses and polarizabilities have been analyzed and compared further.

Metal acetylene cluster ions M +(C 2H 2) n as model reactors for studying reactivity of laser-generated transition metal cations

The present study explores the feasibility of utilizing acetylene clusters as model reactors for screening the catalytic activity of transition metal ions towards the polymerization of acetylene. Laser vaporization/ionization is used to generate atomic transition metal cations (M +*) which interact with neutral acetylene clusters to generate M +(C 2H 2) n cluster ions. Evidence is presented for C H bond activation by low-lying excited states of the laser-generated V +, Fe +, Co + and Ni + ions. A sequential addition of acetylene molecules to the activated acetylene monomer within the clusters is proposed as a possible mechanism for polymerization of acetylene, initiated by C H bond activation. The proposed mechanism suggests the intermediacy of C 4H 3 + in the generation of higher hydrocarbon species such as C 6H 4 +, C 6H 5 +, C 8H 6 + and C 8H 7 +. Based on thermodynamic considerations it is expected that the observed hydrocarbon ions would have cyclic structures equivalent to benzene and styrene fragments. Enhanced ion intensities have been observed for V +(C 2H 2) 2, Cr +(C 2H 2) 2, Fe +(C 2H 2) 4, Fe +(C 2H 2) 4, Co +(C 2H 2) 3, Ni +(C 2H 2) 3, and Cu +(C 2H 2) 3 consistent with the formation of stable covalent products formed by metal ion catalyzed polymerization of acetylene clusters. DFT calculations identify the structures of the initially formed trimer ion clusters Fe +(C 2H 2) 3, Co +(C 2H 2) 3 and Ni +(C 2H 2) 3 where the metal cation is embedded in a “cage” created by the three acetylene molecules. Isomerization of these cluster ions into the more stable metal ion–benzene adducts is suggested and the energy needed to surpass the isomerization barriers is likely to come from the laser-generated excited state metal ions. A remarkable even–odd alternation has been observed for Co +(C 2H 2) n clusters with enhanced ion intensities for n = 3, 6, 9 and 12, which could be explained by multiple isomerization events resulting in the formation of Co +(benzene) n clusters with n = 1–4. The combination of the excited state energy of the TM ions and the unique cluster environment which promotes concerted multi-monomer interactions with the metal ions could lead, under favorable conditions, to TM ion-mediated cyclotrimerization of acetylene molecules resulting in the formation of benzene and other polycyclic aromatic hydrocarbons.

ChemInform Abstract: Geometries and Energies of GeHn and GeH+ n (n = 1-4)

Complete active space MCSCF (multiconfiguration self‐consistent field) (CASSCF) followed by second‐order configuration interaction (SOCI) and multireference singles and doubles CI (MRSDCI) are carried out on the ground states of GeHn and GeH+n (n=1–4). The equilibrium geometries of these species, adiabatic ionization potentials, and stepwise bond energies [De(Hn−1Ge–H) and De(Hn−1Ge+–H)] are calculated. The ground sate of GeH+4 is a Jahn–Teller distorted 2A1(C2v) state with a GeH+2⋅H2 complex structure. The adiabatic ionization potentials (IPS) of GeHn exhibit even–odd alternation. GeH4 is the most stable among the neutral GeHn species while GeH+3 is the most stable of the GeH+n.

Tris(β-diketonates) lanthanum nematic adducts

A series of new liquid-crystalline adducts of lanthanum tris(β-diketonates) displaying nematic and smectic mesomorphism was synthesised and investigated. The temperatures and thermodynamic parameters of the phase transitions were determined. Even–odd alternation of the nematic–isotropic transition was observed in the series of synthesised complexes. It was found that films of the obtained liquid-crystal complexes are vitrified when cooling, and packings of molecules, formed in the mesophase, are retained. Interlayer distances were determined and a model of packing of molecules in the mesophase was suggested based on data obtained by a small-angle X-ray scattering method.

Incorporation of 2,3-Disubstituted-1,4-Naphthoquinones into the A1 Binding Site of Photosystem I Studied by EPR and ENDOR Spectroscopy

Transient electron paramagnetic resonance and pulsed electron-nuclear double resonance (ENDOR) spectra of the state \( P_{700}^{ \cdot + } A_{1}^{ \cdot - } \) in photosystem I containing a series of non-native naphthoquinones (NQs) are presented. Previous studies have shown that quinones bind to the A1 site with only one of their carbonyl groups H-bonded to the protein and that the asymmetric H-bond produces an odd alternant distribution of the spin density within the quinone. It is known that the native phylloquinone binds with its methyl group meta and its phytyl tail ortho to the H-bonded carbonyl. Monosubstituted NQs with short alkyl chains have been found to bind preferentially with their alkyl side groups meta to the H-bonded carbonyl. The selectivity of the binding site toward methyl and short chain substituents is studied by incorporating disubstituted NQs that have a methyl group at the 2-position and a short chain at the 3-position of the quinone ring. The hyperfine couplings (hfcs) of the methyl group protons are sensitive to the spin density distribution on the quinone and are used to deduce the position of the methyl group relative to the H-bonded carbonyl. The measured methyl proton hfcs indicate that the disubstituted quinones bind exclusively with their methyl group in the meta position relative to the H-bonded carbonyl and no evidence for binding with the methyl group in the ortho position is found. The disubstituted quinones have also been chosen to study the effect of electron withdrawing substituents on the spin density distribution. When the short chain contains electronegative atoms such as sulfur or chlorine, the methyl proton hfcs of the quinone in the A1 binding site are found to be significantly larger than those of 2-methyl-1,4-naphthoquinone and phylloquinone in the same environment. Solution ENDOR measurements of the quinone radical anions in isopropanol and density functional theory (DFT) calculations in vacuo show that this increase in the hfcs is mostly intrinsic to the quinones due to the electron-withdrawing ability of the short chain and is not a result of differences in the binding to the protein. The DFT calculations suggest that the main reason for the increased methyl proton hfcs is delocalization of the singly occupied molecular orbital onto the side chain, which leads to an increase of the spin density on the neighboring carbon, which carries methyl group.

A density functional theory study of the Au 7H n ( n = 1–10) clusters

The geometries, electronic, and magnetic properties of the Au 7H n ( n = 1–10) clusters have been systematically investigated by using relativistic all-electron density functional theory with generalized gradient approximation. It is found that the Au 7 on the whole retains its triangle structure after hydrogen atoms adsorption and adsorbing hydrogen atoms can stabilize the Au 7 structure. The Au 7H 7 cluster is much higher stability than the neighboring clusters. The pronounced even–odd alternation of the magnetic moments is observed in the Au 7H n systems indicating Au 7H n clusters possess tunable magnetic properties by adding even or odd number of H atoms.