Density functional theory study of the structures,electronic states and stabilities of Al n Pt (n = 1–15) clusters

The binding energy, dissociation energy, ionization potentials, electron affinities, gap and stability of small Al _n Pt (n = 1–15) clusters, in comparison with pure aluminum clusters have been systematically investigated by means of density functional calculations at the B3LYP level. The growth patten for Al _n Pt clusters is that the Pt atom substituted the surface atom of the Al _{n + 1} clusters for n < 13. Starting from n = 13, the Pt atom completely falls into the center of the Al-frame. The Pt atom substituted the center atom of the Al _{n + 1} clusters to form the Pt-encapsulated Aln geometries for n > 13. We also find that the impurity Pt atom causes local structural distortion due to different atomic radii and different bonding characteristics. The clusters with total atom numbers of 2, 7, and 11 exhibit high stability.     

Structures,stabilities, and electronic properties of Al n Au (n = 1–15) clusters: A density functional study

We present density functional calculations of Al _n Au clusters for n = 1–15. The growth pattern for Al _n Au (n = 1–7, 12, 14, 15) clusters is the Au atom occupying a peripheral position of Al _n clusters, and the growth pattern for Al _n Au (n = 8, 10 and 13) clusters is Au-substituted Al _n+1 clusters. It is found that the Au atom replaces the surface atom of an Al _n+1 cluster and occupies a peripheral position. In addition, the ground state structures of Al _n Au clusters are more stable than pure Aln clusters. It is found that the Al₁₃Au cluster exhibits high stability.     

Structure, Electronic Properties and Interaction of MRn n + (n?=?1–3, M?=?Cu, Ag and Au) Clusters: Ab Initio Calculations

The structures and stabilities of MRn _n ⁺ (n?=?1–3, M?=?Cu, Ag and Au) series at the CCSD(T) theoretical level are performed. The n?=?2 systems are more stable than its neighbours. The role of the interaction is investigated using the natural bond orbital analysis, Laplacian, electron localization function and reduced density gradient analysis. The results show the intermediate character in the M–Rn interaction.     

Structure and stability of AuXe n Z (n = 1–3, Z = −1, 0, +1) clusters

We have explored the structures and stabilities of AuXe _n ^Z (n = 1–3, Z = ?1, 0, +1) cluster series at CCSD(T) theoretical level. The electron affinities and ionization potentials are correlated to the HOMO–LUMO gaps. The role of the interaction was investigated using the natural bond orbital analysis.     

Density functional study on structures, stabilities, and electronic properties of size-selected Pd n Si q (n = 1–7 and q = 0, +1, −1) clusters

The density functional theory (DFT) calculations within the framework of generalized gradient approximation have been employed to systematically investigate the geometrical structures, stabilities, and electronic properties of Pd _n Si ^q (n = 1–7 and q = 0, +1, ?1) clusters and compared them with the pure ${\text{Pd}}_{n + 1}^{q}$ (n = 1–7 and q = 0, +1, ?1) clusters for illustrating the effect of doping Si atom into palladium nanoclusters. The most stable configurations adopt a three-dimensional structure for both pure and Si-doped palladium clusters at n = 3–7. As a result of doping, the Pd _n Si clusters adopt different geometries as compared to that of Pd _n+1. A careful analysis of the binding energies per atom, fragmentation energies, second-order difference of energies, and HOMO–LUMO energy gaps as a function of cluster size shows that the clusters ${\text{Pd}}_{4}^{ + }$ , ${\text{Pd}}_{4}$ , ${\text{Pd}}_{8}^{ - }$ , ${\text{Pd}}_{5} {\text{Si}}^{0, + , - }$ , and ${\text{Pd}}_{7} {\text{Si}}^{0, + , - }$ possess relatively higher stability. There is enhancement in the stabilities of palladium frameworks due to doping with an impurity atom. In addition, the charge transfer has been analyzed to understand the effect of doped atom and compared further.     

A computational study on CunN0,±1 (n=1–4) clusters by density functional methods

Clusters of the type Cu_nN^0,±1 (n=1–4) are investigated computationally using density functional theory methods. Equilibrium geometries are optimized under the constraint of well-defined point-group symmetries at the B3LYP level employing a pseudo-potential method in conjunction with double-zeta basis sets. In this article, different molecular properties such as total energies, electron affinities, ionization potentials, fragmentation energies and equilibrium geometries of the Cu_nN^0,±1 (n=1–4) clusters are systematically calculated and discussed. In particular, the photoelectron spectra of the anionic Cu_nN⁻¹ (n=2–4) clusters are calculated showing a good agreement with the available experimental results. In addition, Mulliken and natural orbital population analyses, and natural orbital configurations are calculated in order to elucidate the charge distributions in the clusters.     

The reaction between HO and (H2O) n (n?=?1, 3) clusters: reaction mechanisms and tunneling effects

The reaction between the HO radical and (H₂O)n (n?=?1, 3) clusters has been investigated employing high-level quantum mechanical calculations using DFT-BH&HLYP, QCISD, and CCSD(T) theoretical approaches in connection with the 6-311?+?G(2df,2p), aug-cc-pVTZ, and aug-cc-pVQZ basis sets. The rate constants have also been calculated and the tunneling effects have been studied by means of time?Cdependent wavepacket calculations, performed using the Quantum?CReaction Path Hamiltonian method. According to the findings of previously reported theoretical works, the reaction between HO and H₂O begins with the formation of a pre-reactive complex that is formed before the transition state, the formation of a post-reactive complex, and the release of the products. The reaction between HO and (H₂O)₂ also begins with the formation of a pre-reactive complex, which dissociates into H₂O??HO?+?H₂O. The reaction between HO and (H₂O)₃ is much more complex. The hydroxyl radical adds to the water trimer, and then it occurs a geometrical rearrangement in the pre-reactive hydrogen-bonded complex region, before the transition state. The reaction between hydroxyl radical and water trimer is computed to be much faster than the reaction between hydroxyl radical and a single water molecule, and, in both cases, the tunneling effects are very important mainly at low temperatures. A prediction of the atmospheric concentration of the hydrogen-bonded complexes studied in this work is also reported.     

Interactions between Ni n (n = 1–4) clusters and molecules of methane,water, and hydrogen peroxide

Quantum chemical computations and study of IR spectra of systems Ni₄ + CH₄, Ni₄ + H₂O, and Ni₄ +H₂O are performed. The results are discussed conjointly with analogous data for products of reactions with Ni _n (n=1–3). It is shown that formation of complexes with either hydrogen atoms or CH₃ and OH radicals in a bridged position is characteristic of these systems. It is essential that the ground state of the nickel frame formed in Ni₄ systems has the form of a flat rhombus, which is different from the main isomer form of Ni₄ having pyramidal structure.     

First-principles study on the geometries,stabilities and electronic properties of yttrium–silicon clusters (Y2Si n ; 1 ≤ n ≤ 12)

Structural Chemistry - The geometries, growth patterns, relative stabilities and electronic properties of yttrium-doped silicon clusters Y2Si n (n&nbsp;=&nbsp;1–12) are systematically...     

The geometric, energetic, and electronic properties of charged phosphorus-doped silicon clusters, PSi n +/PSi n ? (n?=?1�C8)

Charged phosphorus-doped small silicon clusters, PSi _n ⁺/PSi _n ^? (n?=?1?8), have been investigated using the B3LYP/6-311+G* level Kohn?CSham density functional theory (KS-DFT) method. For comparison, the geometries of neutral PSi _n clusters were also optimized at the same level, though most of them have been previously reported. According to our results, cationic PSi _n ⁺ clusters have ground state structures similar to those of pure silicon clusters Si _n+1, with the exception of n?=?5. For anionic PSi _n ^?, most of the lowest-energy structures are in accord with Wade??s 2N+2 rule for closed polyhedra: PSi₄ ^?, PSi₅ ^?, PSi₆ ^?, and PSi₈ ^?, respectively, favor the trigonal bipyramid, tetragonal bipyramid, pentagonal bipyramid, and tricapped trigonal prism (TTP) structures, corresponding to Wade??s 2N+2 rule with N?=?5, 6, 7, and 9. The structures tend to contract when the cationic species is reduced initially to the neutral species and subsequently to the anionic species, implying a strengthening interaction between atoms within the clusters on one and two electron reductions of the cationic species to the neutral and anionic species, respectively. The relative order of stability of the PSi _n ⁺/PSi _n ^? isomers differs from that of the PSi _n isomers. Cluster stability was also analyzed by adiabatic ionization potentials (AIP), adiabatic electron affinities (AEA), binding energies (BE), second-order energy differences (?₂E), and HOMO-LUMO gap values. The results indicate that PSi₄ ^? and PSi₇ ^? clusters are more stable than their neighboring anionic clusters and would be potential species for further mass spectrometric measurements.     

Quantum chemical topology investigation on structure, electronic properties and interaction of CuNg n + (n?=?1–3, Ng?=?He, Ne)

The structures and stabilities of title clusters have been investigated at CCSD(T) computational level. For the title systems, the geometry with high symmetry is preferred and the n?=?2 systems are more stable than its neighbors. For the Cu?CNg interaction, topological analysis of the electron density field, electron localization function, and positive local energy density represent the intermediate interaction type $ \left( {\nabla^{2}{}_{(3,\; - 1)} \rho > 0\; {\text{and}}\;E\left( r \right) < 0} \right) $ . The interaction region is located by generating reduced density gradient isosurface in the real molecular space.     

Bond indices,enthalpies and relative stabilities of real and hypothetical closo-BnHc−n clusters (n = 5–12; c = 0, 2 or 4) as revealed by the molecular-orbital bond index method

Bond indices (I) have been calculated, using the CNDO-based molecular-orbital bond index method, for real and hypothetical closo borane species, B_nH^c−_n (n = 5–12; c = 0, 2 or 4), and used to infer their relative stabilities by means of the bond index (I)bond enthalpy [E (kJ mol⁻¹)] equations E(BB) = 297.9I(BB) and E(BH) = 374.8I(BH). For the species able to tolerate n + 2 skeletal electron pairs (n = 8, 9 or 11) in closed-shell electronic configurations, estimates of the relative stabilities of alternative nido structures for the anions B_nH⁴⁻_n have been made. Detailed assessments of the changes in bond index with electron numbers of particular edge types for B_nH^c−_n species (n = 8, 9 or 11; c = 0, 2 or 4) have been carried out, providing quantitative confirmation of earlier qualitative predictions, and showing that generally for the “normal” closo B_nH²⁻_n species addition or removal of an electron pair leads to the same type of polyhedral distortion, because, where the HOMO of B_nH²⁻_n is bonding for a particular edge, the LUMO is antibonding.     

Interaction behavior study of HCl on (ZnS)n (n = 1–12) clusters and HCl effect on Hg0 adsorption

The interaction behavior of HCl and (ZnS)_n (n = 1–12) clusters and HCl effect on Hg⁰ adsorbed by (ZnS)_n have been studied theoretically. The combined genetic algorithm and density functional theory (GA-DFT) method has been used to obtain the structures of (ZnS)_nHCl and (ZnS)_nHgHCl (n = 1–12) clusters. The structural properties of (ZnS)_nHCl and (ZnS)_nHgHCl have been analyzed. The adsorption energies and interaction energies have been calculated. Bond length and bond order analysis has revealed that S H and Zn Cl bonds form after HCl adsorbed on (ZnS)_n clusters, while Hg⁰ can only weakly bind with (ZnS)_nHCl clusters. According to thermodynamic adsorption analysis, the formation of (ZnS)_nHCl clusters from (ZnS)_n and HCl are spontaneous because of their negative Gibbs free energy changes. The formation of (ZnS)_nHgHCl from (ZnS)_nHCl and Hg are nonspontaneous for n = 1–4 and 9, and the Gibbs free energy changes have small negative values for other sizes. Electron localization function and noncovalent interaction (NCI) analysis of (ZnS)₁₀HgHCl manifest that Hg and its nearest Zn form zinc amalgam. Projected density of state study has been performed to obtain the interaction nature of HCl and (ZnS)_n clusters and Hg⁰ adsorption on (ZnS)_nHCl clusters. Based on our study, HCl is chemical adsorbed by (ZnS)_n clusters except (ZnS)₄ cluster. After (ZnS)_n adsorbs HCl, Hg⁰ can physically adsorb on (ZnS)_nHCl clusters. The strength of Hg⁰ on (ZnS)_nHCl is comparable to that of Hg⁰ on (ZnS)_n, indicating that HCl can hardly affect the adsorption of Hg⁰ on ZnS clusters.     

Geometries and stabilities of transition metals doped perfect and Stone–Wales defective armchair (5,5) boron nitride nanotubes

The binding abilities of transition metals (TMs) (TMs?=?Ni, Pd, and Pt) on perfect and Stone?CWales (SW) defective armchair (5,5) single-walled boron nitride nanotubes (BNNTs) were investigated using density functional theory method at the B3LYP/LanL2DZ level. The geometrical parameters and electronic properties of all BNNTs doped with TM atoms are reported. The strongest binding energy of Ni doped on SW defective BNNT of ?91.87?kcal/mol was found. The binding abilities of the most stable of TMs on the BNNTs are in order: Ni/SW2?CBNNT(Z_N)?>?Pt/SW2?CBNNT(Z_B)?>?Pd/SW2?CBNNT(Z_B). In all case, energy gaps of MTs doped perfect and defective BNNTs are obviously lower than their undoped nanotubes.     

Theoretical study of silicon–sulfur clusters (SiS2)n (n = 1–6)

 The possible geometrical structures and relative stability of (SiS₂) _n (n=1–6) silicon–sulfur clusters are explored by means of density functional theory quantum chemical calculations. The effects of polarization functions and electron correlation are included in these calculations. The electronic structures and vibrational spectra of the most stable geometrical structures of (SiS₂) _n are analyzed by the same method. As a result, the regularity of the (SiS₂) _n cluster growth is obtained, and the calculation may used for predicting the formation mechanism of the (SiS₂) _n cluster. Received: 17 November 1999 / Accepted: 3 November 2000 / Published online: 3 May 2001     

Ab Initio Study of Neutral and Charged Copper Bromide (CuBr) n (+) Clusters (n?=?1–6)

A theoretical study in the framework of the density functional theory is performed to investigate the stability, the structural and electronic properties of both neutral and cationic copper bromide clusters (CuBr) _n ⁽⁺⁾, n = 1–6. The most stable isomers are found to be cyclic arrangements. Calculated infrared frequencies are compared with the available experimental spectra. The nature of the ionio-covalent bonding is characterized. The fragmentation, the ionization potentials are also investigated.     

Searching new structures of beryllium-doped in small-sized magnesium clusters: Be2MgnQ (Q = 0, −1; n = 1–11) clusters DFT study

Using CALYPSO method to search new structures of neutral and anionic beryllium-doped magnesium clusters followed by density functional theory (DFT) calculations, an extensive study of the structures, electronic and spectral properties of Be₂Mg_n^Q (Q = 0, −1; n = 2–11) clusters is performed. Based on the structural optimization, it is found that the Be₂Mg_n^Q (Q = 0, −1) clusters are shown by tetrahedral-based geometries at n = 2–6 and tower-like-based geometries at n = 7–11. The calculations of stability indicate that Be₂Mg₅^Q=0, Be₂Mg₅^Q=−1, and Be₂Mg₈^Q=−1 clusters are “magic” clusters with high stability. The NCP shows that the charges are transferred from Mg atoms to Be atoms. The s- and p-orbitals interactions of Mg and Be atoms are main responsible for their NEC. In particular, chemical bond analysis including molecular orbitals (MOs) and chemical bonding composition for magic clusters to further study their stability. The results confirmed that the high stability of these clusters is due to the interactions between the Be atom and the Mg₅ or Mg₈ host. Finally, theoretical calculations of infrared and Raman spectra of the ground state of Be₂Mg_n^Q (Q = 0, −1; n = 1–11) clusters were performed, which will be absolutely useful for future experiments to identify these clusters.     

Influence of the Length of the Alanine Spacer on the Acidic–Basic Properties of the Ac–Lys–(Ala) n –Lys–NH2 Peptides (n?=?0, 1, 2, …, 5)

By using the potentiometric titration method, we have determined the pK _a values of the two terminal lysine groups in six alanine-based peptides differing in the length of the alanine chain: Ac?CLys?CLys?CNH₂ (KK), Ac?CLys?CAla?CLys?CNH₂ (KAK), Ac?CLys?CAla?CAla?CLys?CNH₂ (KAK2), Ac?CLys?CAla?CAla?CAla?CLys?CNH₂ (KAK3), Ac?CLys?CAla?CAla?CAla?CAla?CLys?CNH₂ (KAK4), and Ac?CLys?CAla?CAla?CAla?CAla?CAla?CLys?CNH₂ (KAK5) in aqueous solution. For each compound, the model of two stepwise acid?Cbase equilibria was fitted to the potentiometric-titration data. As expected, the pK _a values of the lysine groups increase with increasing length of the alanine spacer, which means that the influence of the electrostatic field between one charged group on the other decreases with increasing length of the alanine spacer. However, for KAK3, the pK _a1 value (8.20) is unusually small and pK _a2 (11.41) is remarkably greater than pK _a1, suggesting that the two groups are close to each other and, in turn, that a chain-reversal conformation is present for this peptide. Starting with KAK3, the differences between pK _a1 and pK _a2 decrease; however, for the longest peptide (KAK5), the values of pK _a1 and pK _a2 still differ by about 1 unit, i.e., by more than the value of log₁₀ (4)?=?0.60 that is a limiting value for the pK _a difference of dicarboxylic acids with increasing methylene-spacer length. Consequently, some interactions between the two charged groups are present and, in turn, a bent shape occurs even for the longest of the peptides studied.     

Growth behavior and properties of (HF)1–16 clusters

Structural Chemistry - HF cluster is a typical hydrogen bond system. (HF)1–16 clusters have been studied by MP2/aug-cc-pvdz//B3LYP/6-311++G(d,p) method. The global minimum structures of them...