A systematic search for the structures,stabilities, and electronic properties of bimetallic Ca<Subscript>2</Subscript>-doped gold clusters: comparison with pure gold clusters

The local meta-GGA exchange correlation density functional (TPSS) with a relativistic effective core potential was employed to systematically investigate the geometric structures, stabilities, and electronic properties of bimetallic Ca₂Au _n (n = 1–9) and pure gold Au _n (n ≤ 11) clusters. The optimized geometries show that the most stable isomers for Ca₂Au _n clusters have 3D structure when n > 2, and that one Au atom capping the Ca₂Au _n−1 structure for different-sized Ca₂Au _n (n = 1–9) clusters is the dominant growth pattern. The average atomic binding energies and second-order difference in energies show that the Ca₂Au₄ isomer is the most stable among the Ca₂Au _n clusters. The same pronounced even–odd alternations are found in the HOMO–LUMO gaps, VIPs, and hardnesses. The polarizabilities of the Ca₂Au _n clusters show an obvious local minimum at n = 4. Moreover, the inverse corrections to the polarizabilities versus the ionization potential and hardness were found for the gold clusters.     

Hydrogen sequential dissociative chemisorption on Nin(n = 2~9,13) clusters: comparison with Pt and Pd

Hydrogen dissociative chemisorption and desorption on small lowest energy Ni_n clusters up to n = 13 as a function of H coverage was studied using density functional theory. H adsorption on the clusters was found to be preferentially at edge sites followed by 3-fold hollow sites and on-top sites. The minimum energy path calculations suggest that H₂ dissociative chemisorption is both thermodynamically and kinetically favorable and the H atoms on the clusters are mobile. Calculations on the sequential H₂ dissociative chemisorption on the clusters indicate that the edge sites are populated first and subsequently several on-top sites and hollow sites are also occupied upon full cluster saturation. In all cases, the average hydrogen capacity on Ni_n clusters is similar to that of Pd_n clusters but considerably smaller than that of Pt_n clusters. Comparison of hydrogen dissociative chemisorption energies and H desorption energies at full H-coverage among the Ni family clusters was made.     

Chemisorptions effect of oxygen on the geometries,electronic and magnetic properties of small size Nin (n = 1-6) clusters

The present study reports the effect of oxygen addition on small size Ni_n (n = 1-6) clusters in different spin states within the framework of linear combination of atomic orbital (LCAO) density functional theory (DFT) under spin polarized generalized gradient approximation (GGA) functional. Relative stabilities of the optimized clusters are discussed on the basis of the calculated parameters, such as, binding energy (BE), embedding energy (EE) and fragmentation energy (FE). Other parameters, like ionization potential (IP), electron affinity (EA), etc. show that though the additions of oxygen can affect the chemical properties of Ni_n clusters with an additional stability to Ni_nO. In most of the cases the magnetic moment of the stable isomers are geometry dependent for a particular size both in pure and oxidized clusters. Calculated magnetic moments of Ni_nO (n = 1-6) clusters reveal that the magnetic moment of ground state Ni₄O isomers in different geometries is same as in pure Ni₄ isomers. Present study also explains the cause of stable magnetic moment in Ni₄O cluster through the distribution of electrons in different orbitals.     

The adsorption of mercury-species on relaxed and rumpled CaO (0 0 1) surfaces investigated by density functional theory

This research examines the importance of several computational choices in modeling mercury species adsorption on calcium oxide surfaces and is the second in a series of papers. The importance of surface relaxation was tested and it was found that adsorption energies changed for HgCl₂, moving adsorption from being at the borderline of physisorption and chemisorption to being strongly chemisorbed. Results for Hg and HgCl were unaffected. A second computational choice, that of the cluster or periodic model size was tested in both the plane of the model (4 × 4 or 5 × 5 model sizes) and for the depth (two or three layers). It was found that the minimum cluster size for handling mercury adsorption was 5 × 5 and that only two layers of depth were needed. The energetic results show that rumpled CaO surfaces will only weakly physisorb elemental mercury, but could be used to capture HgCl₂ from coal combustion flue gases, which is in agreement with limited experimental data.     

All-electron scalar relativistic calculation of water molecule adsorption onto small gold clusters

An all-electron scalar relativistic calculation was performed on Au _n H₂O (n = 1–13) clusters using density functional theory (DFT) with the generalized gradient approximation at PW91 level. The calculation results reveal that, after adsorption, the small gold cluster would like to bond with oxygen and the H₂O molecule prefers to occupy the single fold coordination site. Reflecting the strong scalar relativistic effect, Au _n geometries are distorted slightly but still maintain a planar structure. The Au–Au bond is strengthened and the H–O bond is weakened, as manifested by the shortening of the Au–Au bond-length and the lengthening of the H–O bond-length. The H–O–H bond angle becomes slightly larger. The enhancement of reactivity of the H₂O molecule is obvious. The Au–O bond-lengths, adsorption energies, VIPs, HLGs, HOMO (LUMO) energy levels, charge transfers and the highest vibrational frequencies of the Au–O mode for Au _n H₂O clusters exhibit an obvious odd-even oscillation. The most favorable adsorption between small gold clusters and the H₂O molecule takes place when the H₂O molecule is adsorbed onto an even-numbered Au _n cluster and becomes an Au _n H₂O cluster with an even number of valence electrons. The odd–even alteration of magnetic moments is observed in Au _n H₂O clusters and may serve as material with a tunable code capacity of “0” and “1” by adsorbing a H₂O molecule onto an odd or even-numbered small gold cluster.     

Density functional theory study of small nickel clusters

The stable geometries and atomization energies for the clusters Ni _n (n = 2–5) are predicted with all-electron density functional theory (DFT), using the BMK hybrid functional and a Gaussian basis set. Possible isomers and several spin states of these nickel clusters are considered systematically. The ground spin state and the lowest energy isomers are identified for each cluster size. The results are compared to available experimental and other theoretical data. The molecular orbitals of the largest cluster are plotted for all spin states. The relative stabilities of these states are interpreted in terms of superatom orbitals and no-pair bonding.     

Ab initio investigations on planar (MgO)n clusters (n = 1–5) and their hydrogen adsorption behaviour

Ab initio calculations (B3LYP and PBE-D3) of the structures, stabilities, vibrational, electronic and hydrogen adsorption behaviour of (MgO)_n clusters are performed using 6-311+ + G(d,p) basis set. The planar (MgO)_n clusters are found to be global minima for n ≤ 3 and local minima for n = 4 and 5. In addition, we have also analysed global minimum structures of (MgO)₄ and (MgO)₅. The binding energies suggest that their stabilities increase successively. Vibrational frequencies and IR intensities further support the enhanced stability with an increase in the size of (MgO)_n clusters. The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) surfaces are used to explain and discuss the electronic properties. Finally, we have demonstrated hydrogen storage capacity of (MgO)_n clusters, considering hydrogen adsorption on planar as well as global minimum (MgO)₄ and (MgO)₅ clusters. We have noticed that four and five H₂ molecules can be easily adsorbed by (MgO)₄ and (MgO)₅ clusters having adsorption energy of 0.13–0.14 eV with mass ratio of 4.76%. Thus, the present study is expected to motivate further the applications of small clusters for efficient hydrogen energy storage.     

Adsorption and spin state properties of Cr,Ni, Mo,and Pt deposited on Li+ and Na+ monovalent cation impurities of MgO (001) surface: DFT calculations

We have analyzed, by means of density functional theory calculations and the embedded cluster model, the adsorption and spin-state properties of Cr, Ni, Mo, and Pt deposited on a MgO crystal. We considered deposition at the Mg²⁺ site of a defect-free surface and at Li⁺ and Na⁺ sites of impurity-containing surfaces. To avoid artificial polarization effects, clusters of moderate sizes with no border anions were embedded in simulated Coulomb fields that closely approximate the Madelung fields of the host surfaces. The interaction between a transition metal atom and a surface results from a competition between Hund's rule for the adsorbed atom and the formation of a chemical bond at the interface. We found that the adsorption energies of the metal atoms are significantly enhanced by the cation impurities, and the adsorption energies of the low-spin states of spin-quenched complexes are always more favorable than those of the high-spin states. Spin polarization effects tend to preserve the spin states of the adsorbed atoms relative to those of the isolated atoms. The metal–support interactions stabilize the low-spin states of the adsorbed metals with respect to the isolated metals, but the effect is not always enough to quench the spin. Spin quenching occurs for Cr and Mo complexes at the Mg²⁺ site of the pure surface and at Li⁺ and Na⁺ sites of the impurity-containing surfaces. Variations of the spin-state properties of free metals and of the adsorption and spin-state properties of metal complexes are correlated with the energies of the frontier orbitals. The electrostatic potential energy curves provide further understanding of the nature of the examined properties.     

Ab initio calculation of the geometries, stabilities, and electronic properties for the bimetallic Be2Au(n) (n = 1-9) clusters: comparison with pure gold clusters

Ab initio methods based on density functional theory at BP86 level were applied to the study of the geometrical structures, relative stabilities, and electronic properties of small bimetallic Be₂Au _n (n = 1–9) clusters. The optimized geometries reveal that the most stable isomers have 3D structures at n = 3, 5, 7, 8, and 9. Here, the relative stabilities were investigated in terms of the averaged atomic binding energies, fragmentation energies and second-order difference of energies. The results show that the planar Be₂Au₄ structure is the most stable structure for Be₂Au _n clusters. The HOMO−LUMO gap, vertical ionization potential, vertical electron affinity and chemical hardness exhibit a pronounced even–odd alternating phenomenon. In addition, charge transfer and natural electron configuration were analyzed and compared.     

A DFT study on equilibrium geometries, stabilities, and electronic properties of small bimetallic Na-doped Au(n) (n = 1-9) clusters: comparison with pure gold clusters

A systematic study on the geometric structures, relative stabilities, and electronic properties of small bimetallic Au _n Na (n = 1-9) clusters has been performed by means of first-principle density functional theory calculations at the PW91PW91 level. The results show that the optimized ground-state isomers adopt planar structures up to n = 5, and the Na-capped geometries are dominant growth patterns for n = 6-9. Dramatic odd-even alternative behaviors are obtained in the second-order difference of energies, fragmentation energies, highest occupied-lowest unoccupied molecular orbital energy gaps, and chemical hardness for both Au _n Na and Au _n+1 clusters. It is found that Au₅Na and Au₆ have the most enhanced stability. Here, the size evolutions of the theoretical ionization potentials are in agreement with available experimental data, suggesting a good prediction of the lowest energy structures in the present study. In addition, the charge transfer has been analyzed on the basis of natural population analysis.     

Elucidation of the molecular and electronic structures of some magic silver clusters Ag<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 8, 18, 20)

Density functional theory (DFT) calculations were carried out to explore the geometric, spectroscopic, and electronic properties of three magic silver clusters Ag_n (n?=?8, 18, and 20) in detail. The computed results show that the global minima of these clusters are compact, near-spherical structures, while other low-lying isomers exhibit oblate or prolate shapes. Vertical ionization energies for the low-lying isomers were also computed and assigned with respect to available experimental values. Although several isomers were predicted to have similar energies, their electronic and vibrational signatures were quite distinctive, meaning that they could be used as fingerprint signals to distinguish between isomers. In addition, the electronic structures of these systems were explored using the phenomenological shell model. Calculations for the coinage metal clusters M₂₀ (M?=?Cu, Ag, Au) indicated that the structures and properties of the Ag cluster are similar to those of the Cu cluster in that both Cu₂₀ and Ag₂₀ prefer a compact structure whereas Au₂₀ prefers to adopt a tetrahedral form.

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Graphical abstract Shell Orbitals of Ag₈ Cluster

     

Structures of Au/Pt bimetallic clusters: homogeneous or segregated?

The question whether Au can alloy with Pt at the nano-scale size is still controversial. By performing density functional theory calculations for several small Au/Pt bimetallic clusters Au_mPt_n (m + n = 4–6, 13), we find that, in all the most stable geometries, Pt atoms prefer to assemble together to form the core while Au atoms like to surround the Pt atoms to form the shell, and that evenly mixed clusters are structurally unstable. The unique geometric characteristics can be explained by analyzing the different electronic properties of Pt–Pt, Au–Pt and Au–Au bonds, and is expected also to apply to larger Au/Pt bimetallic clusters.     

Theoretical study on the structural,vibrational, and thermodynamic properties of the (Br<Subscript>2</Subscript>GaN<Subscript>3</Subscript>)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1–4) clusters

The molecular geometries, vibrational properties, and thermodynamic properties of the clusters (Br₂GaN₃) _n (n = 1–4) were studied at the B3LYP/6-311+G* level. The optimized clusters (Br₂GaN₃) _n (n = 2–4) were all found to possess a cyclic structure consisting of Ga atoms bridged by the α-nitrogen of the azide groups. A discussion of the relationships between the geometrical parameters and the degree of oligomerization n is provided. Features in the IR spectra were assigned by vibrational analysis. Trends in thermodynamic properties with temperature and degree of oligomerization n are discussed. Thermodynamic analysis of the gas-phase reaction showed that the formation of the clusters (Br₂GaN₃) _n (n = 2–4) is thermodynamically favorable considering the enthalpies at 298.2 K. The calculated results for the Gibbs free energies were negative, which indicates that the oligomerizations can occur spontaneously at 298.2 K.     

Architecture, electronic structure and stability of TM@Ge(n) (TM = Ti, Zr and Hf; n = 1-20) clusters: a density functional modeling

The present study reports the geometry, electronic structure and properties of neutral and anionic transition metal (TM = Ti, Zr and Hf)) doped germanium clusters containing 1 to 20 germanium atoms within the framework of linear combination of atomic orbitals density functional theory under spin polarized generalized gradient approximation. Different parameters, like, binding energy (BE), embedding energy (EE), energy gap between the highest occupied and lowest unoccupied molecular orbitals (HOMO-LUMO), ionization energy (IP), electron affinity (EA), chemical potential etc. of the energetically stable clusters (ground state cluster) in each size are calculated. From the variation of these parameters with the size of the clusters the most stable cluster within the range of calculation is identified. It is found that the clusters having 20 valence electrons turn out to be relatively more stable in both the neutral and the anionic series. The sharp drop in IP as the valence electron count increases from 20 to 21 in neutral cluster is in agreement with predictions of shell models. To study the vibrational nature of the clusters, IR and Raman spectrum of some selected TM@Ge_n (n = 15,16,17) clusters are also calculated and compared. In the end, relevance of calculated results to the design of Ge-based super-atoms is discussed.     

Intermolecular interactions between gold clusters and selected amino acids cysteine and glycine: a DFT study

The intermolecular interactions between Au_n (n = 3–4) clusters and selected amino acids cysteine and glycine have been investigated by means of density functional theory (DFT). Present calculations show that the complexes possessing Au-NH₂ anchoring bond are found to be energetically favored. The results of NBO and frontier molecular orbitals analysis indicate that for the complex with anchoring bonds, lone pair electrons of sulfur, oxygen, and nitrogen atoms are transferred to the antibonding orbitals of gold, while for the complex with the nonconventional hydrogen bonds (Au···H–O), the lone pair electrons of gold are transferred to the antibonding orbitals of O-H bonds during the interaction. Furthermore, the interaction energy calculations show that the complexes with Au-NH₂ anchoring bond have relatively high intermolecular interaction energy, which is consistent with previous computational studies.     

The impact of Cu atoms on the reactivity of ZrO2 oligomers

A theoretical study on (ZrO₂) _n (n = 1–5) and Cu/ZrO₂ oligomers is presented, DFT/B3LYP/6-31G** calculations along with Lanl2DZ pseudopotentials on metallic centers have been used to predict ionization potentials and electron affinities, chemical potentials and bandgaps indicating that the reactivity reaches reasonably constant values at n = 5. The effect of copper atoms adsorbed on (ZrO₂) _n is discussed and the reactivity of oligomers of ZrO₂ and Cu/ZrO₂ are compared, results indicate that Cu activates the systems by localizing the specific nucleophilic and electrophilic reactivity.     

Search for structures,potential energy surfaces,and stabilities of planar B<Subscript>n</Subscript>P(n = 1 ∼ 7)

We have systematically explored and investigated the geometrical structures, stability, growth pattern, bonding character, and potential energy surface (PES) of the possible isomers of each cluster for planar B_nP (n = 1 ∼ 7) at the CCSD(T)/6-311+;G(d)//B3LYP/6-311+G(d) level. A large number of planar structures for the possible isomers of B_nP (n = 1 ∼ 7) and transition states are located. Isomers 1a ∼ 7a of B_nP are the lowest-energy structures and 2a, 4a, as well as 6a are more stable than their neighbors. For the lowest-energy structures (1a ∼ 7a) of B_nP, P atom lies at the apex and tends to form two B-P bonds with boron atoms. They exhibit planar zigzag growth feature or approximately spherical-like growth pattern. Results from molecular orbital analysis demonstrate that the formation of the delocalized π MOs and the σ-radial and σ-tangential MOs plays a critical role in stabilizing the structures of lowest-energy isomers (2a ∼ 7a) of B_nP. Importantly, isomers 3a, 3c, 3d, 4a, 4b, 5b, and 5c of B_nP are stable both thermodynamically and kinetically at the CCSD(T)/6-311+G(d)// B3LYP/6-311+G(d) level and detectable in laboratory, which is valuable for further experimental studies of B_nP.     

Microsolvation effect and hydrogen-bonding pattern of taurine-water TA-(H2O)n (n = 1-3) complexes

The microsolvation of taurine (TA) with one, two or three water molecules was investigated by a density functional theory (DFT) approach. Quantum theory of atoms in molecules (QTAIM) analyses were employed to elucidate the hydrogen bond (H-bond) interaction characteristics in TA-(H₂O)_n (n = 1–3) complexes. The results showed that the intramolecular H-bond formed between the hydroxyl and the N atom of TA are retained in most TA-(H₂O)_n (n = 1–3) complexes, and are strengthened via cooperative effects among multiple H-bonds from n = 1–3. A trend of proton transformation exists from the hydroxyl to the N atom, which finally results in the cleavage of the origin intramolecular H-bond and the formation of a new intramolecular H-bond between the amino and the O atom of TA. Therefore, the most stable TA-(H₂O)₃ complex becomes a zwitterionic complex rather than a neutral type. A many-body interaction analysis showed that the major contributors to the binding energies for complexes are the two-body energies, while three-body energies and relaxation energies make significant contributions to the binding energies for some complexes, whereas the four-body energies are too small to be significant.     

Ab initio studies on the decomposition kinetics of CF<Subscript>3</Subscript>OCF<Subscript>2</Subscript>O radical

The present study deals with the decomposition of CF₃OCF₂O radical formed from a hydrofluoroether, CF₃OCHF₂ (HFE-125), in the atmosphere. The study is performed using ab initio quantum mechanical methods. Two plausible pathways of decomposition of the titled species have been considered, one involving C-O bond scission and the other occurring via F atom elimination. The geometries of the reactant, products and transition states involved in the decomposition pathways are optimized and characterized at DFT (B3LYP) level of theory using 6-311G(d,p) basis set. Single point energy calculations have been performed at G2M(CC,MP2) level of theory. Out of the two prominent decomposition channels considered, the C-O bond scission is found to be dominant involving a barrier height of 15.3 kcal mol⁻¹ whereas the F-elimination path proceeds with a barrier of 26.1 kcal mol⁻¹. The thermal rate constants for the above two decomposition pathways are evaluated using canonical transition state theory (CTST) and these are found to be 1.78 × 10⁶ s⁻¹ and 2.83 × 10⁻⁷ s⁻¹ for C-O bond scission and F-elimination respectively at 298 K and 1 atm pressure. Transition states are searched on the potential energy surfaces involved during the decomposition channels and each of the transition states is characterized. The existence of transition states on the corresponding potential energy surface is ascertained by performing intrinsic reaction coordinate (IRC) calculation.