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.     

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.     

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.     

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.     

Microsolvation of aminoethanol: a study using DFT combined with QTAIM

The microsolvation of aminoethanol (AE) with one, two, three or four water molecules was investigated using a density functional theory (DFT) approach. Quantum theory of atoms in molecules (QTAIM) analyses were employed to elucidate the hydrogen-bonding characteristics of AE–(H₂O) _n (n = 1–4) complexes. The results showed that AE tends to break its intramolecular OH^AE···N^AE hydrogen bond (H-bond) upon microsolvation and form intermolecular H-bonds with water molecules, while complexes that retain the intramolecular OH^AE···N^AE H-bond show reduced stabilities. The intermolecular H-bond that forms between the nitrogen atom of AE and the hydroxyl of a water molecule is the strongest one for the most stable AE–(H₂O) _n (n = 1–4) complexes, and as n increases from 1 to 4 they grow stronger. The partial covalent character of this H-bond was confirmed by QTAIM analyses. Many-body interaction analysis showed that the relaxation energies and two- and three-body energies make significant contributions to the binding energies of the complexes.     

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.     

Time-dependent density functional theory study of the excited-state dihydrogen bonding: clusters of 2-pyridone with diethylmethylsilane and triethylgermanium

Density functional theory (DFT) was carried out to identify the existence of intermolecular dihydrogen bonds of the 2-pyridone (2PY)-diethylmethylsilane (DEMS) and 2PY-triethylgermanium (TEGH) clusters in the ground state. The H···H distances of both clusters are shorter than the sum of their van der Waals radii. Thus, intermolecular dihydrogen bonds N–H•••H–Si and N–H•••H–Ge exist in the 2PY-DEMS and 2PY-TEGH clusters, respectively. Based on the ground-state conformations, intermolecular dihydrogen bonds N–H•••H–Si and N–H•••H–Ge in the electronically excited state of the 2PY-DEMS and 2PY-TEGH clusters were also investigated using time-dependent density functional theory (TDDFT). Electronic transition of the 2PY-DEMS cluster resembles that of the 2PY-TEGH cluster. Their S₁ state is a locally excited (LE) state centered on 2PY moiety. The H•••H distances of the 2PY-DEMS and 2PY-TEGH clusters both stretch in the S₁ state compared to those in the ground state. Upon electronic excitation, intermolecular dihydrogen bonding N–H•••H–Si and N–H•••H–Ge can weaken with decreasing dihydrogen bonding energies.     

Catalytic mechanisms of Au<Subscript>11</Subscript> and Au<Subscript>11-n</Subscript>Pt<Subscript>n</Subscript> (<Emphasis Type="Italic">n</Emphasis>=1–2) clusters: a DFT investigation on the oxidation of CO by O<Subscript>2</Subscript>

The oxidation of CO catalyzed by clusters of Au₁₁, Au₁₀Pt and Au₉Pt₂ was investigated using the M06 functional suite of the density functional theory. Au and Pt atoms were described with the double-ζ valence basis set Los Alamos National Laboratory 2-double-z (LanL2DZ), whereas the standard 6-311++G(d,p) basis set was employed for the C and O atoms. Our theoretical model showed that (1) after coordination to Au and Au-Pt cluster, O₂ and CO are apparently activated, and Mulliken charges show that the gold atoms in the active sites of Au11 are negatively charged; (2) Au-Pt clusters with 11 atoms can effectively catalyze the oxidation of CO by O₂; (3) Au₁₁ exhibits good catalytic performance for the oxidation of CO; (4) oxidation of CO occurs preferably on the Au–Pt active sites in Pt-doped clusters, and the single-center mechanisms are more favorable energetically than the two-center mechanisms; (5) after adsorption, an O₂ molecule oxidates two CO molecules via stepwise mechanisms; and (6) the catalytic processes are highly exothermic.     

Density functional theory study on (LiNH<Subscript>2</Subscript>)<Subscript>n</Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1–5) clusters

Geometrical structures and relative stabilities of (LiNH₂)_n (n = 1–5) clusters were studied using density functional theory (DFT) at the B3LYP/6-31G* and B3LYP/6-31++G* levels. The electronic structures, vibrational properties, N–H bond dissociation energies (BDE), thermodynamic properties, bond properties and ionization potentials were analyzed for the most stable isomers. The calculated results show that the Li–N and Li–Li bonds can be formed more easily than those of the Li–H or N–H bonds in the clusters, in which NH₂ is bound to the framework of Li atomic clusters with fused rings. The average binding energies for each LiNH₂ unit increase gradually from 142 kJ mol⁻¹ up to about 180 kJ mol⁻¹ with increasing n. Natural bond orbital (NBO) analysis suggests that the bonds between Li and NH₂ are of strong ionicity. Three-center–two-electron Li–N–Li bonding exists in the (LiNH₂)₂ dimer. The N–H BDE values indicate that the change in N–H BDE values from the monomer a1 to the singlet-state clusters is small. The N–H bonds in singlet state clusters are stable, while the N–H bonds in triplet clusters dissociate easily. A study of their thermodynamic properties suggests that monomer a1 forms clusters (b1, c1, d2 and e1) easily at low temperature, and clusters with fewer numbers of rings tend to transfer to ones with more rings at low temperature. E _g, E _HOMO and E _av decrease gradually, and become constant. Ring-like (LiNH₂)_3,4 clusters possess higher ionization energy (VIE) and E _g, but lower values of E _HOMO. Ring-like (LiNH₂)_3,4 clusters are more stable than other types. A comparison of structures and spectra between clusters and crystal showed that the NH₂ moiety in clusters has a structure and spectral features similar to those of the crystal.     

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.     

Effects of the position and manner of hydration on the stability of solvated N-methylacetamides and the strength of binding between N-methylacetamide and water clusters: a computational study

This work mainly studies the effects of the position (there are two possible hydrated sites) and the manner (i.e., whether water acts as a proton donor or acceptor) of hydration by various numbers of water molecules on the stability of 14 solvated N-methylacetamide structures, NMA-(H₂O) _n (n = 1–3), as well as the binding strength between the NMA and the water cluster, using molecular dynamics (MD) and B3LYP methods. Natural bond orbital (NBO) analysis is used to explore the origin of these effects. Some novel observations are obtained from the work. Our results show that monohydration at the carbonyl site favors stability and binding strength compared to monohydration at the amino site. Similarly, the preferred hydration at the carbonyl site is observed for dihydrated NMAs when the second water is added as a proton donor to the C=O group or the first water is H-bonded to the C=O group. However, unfavorable hydration at the C=O site occurs if the second water acts as a proton acceptor. Trihydration by a ring cluster of three water molecules at either the carbonyl site or the amino one yields relatively stable complexes, but significantly disfavors binding strength. The other trihydrated NMAs show similar behavior to dihydrated NMAs. In addition, our results show that the C=O and N–H frequencies can still be utilized to examine the H-bond effects of the water cluster.     

Theoretical studies on the structures,intra- and inter-molecular hydrogen bonding interactions in HNF and HNF–H2O clusters in the gaseous,aqueous and solid phases

Hydrazimium nitroformate ([N₂H₅]⁺[C(NO₂)₃]^? , HNF) is an ionic oxidiser used in solid propellants. Its properties are easily affected by H₂O because of its hygroscopicity. In this article, density functional theory (DFT) and molecular dynamics (MD) were employed to study the isolated HNF molecule and the HNF–H₂O cluster in gas phase and in the aqueous solution. Three stable conformations were obtained for HNF in the gas phase and in the aqueous solution, respectively, and each conformation can form several different HNF–H₂O clusters. Irrespective of whether it is in gas phase or in solution, intramolecular hydrogen bond interactions and other interactions (e.g. the binding energy, the dispersion energy, the second-order perturbation energy and the energy gap between frontier orbitals) of HNF are weaker in the clusters than in the isolated state. The initial decomposition energy of the cluster is lower than that of the isolated HNF molecule in both gaseous and aqueous phases, while the dissociation processes are the same. Molecular dynamic simulations showed that the clustered H₂O elongates and weakens the C–NO₂ bond in the solid HNF–H₂O cluster compared with that in the solid HNF. H₂O reduces and weakens intramolecular N–HΛO bonds too, and O–HΛN is the dominant intermolecular hydrogen bond between HNF and H₂O.     

Bonding and electronic structures in W@Au12AE complexes (AE= NO+, CO, BF, CN–, or BO–): analogies among ligands isoelectronic to carbon monoxide

A theoretical study on the geometries and electronic structures of W@Au₁₂AE (AE=NO⁺, BF, CN^–, or BO^–) was carried out to gain insight into interactions between W@Au₁₂ and ligands isoelectronic with CO. The best configuration for the adsorption site is on-top type for all five complexes. After complexing with boron ligands (BF or BO^–), the axial Au–W bond distance in W@Au₁₂ is lengthened notably, but NO⁺ has the opposite effect on the axial Au–W bond. A charge transfer and energy decomposition analysis shows that the metal–ligand bonds have enhanced σ-donation strength from NO⁺ to BO^–. Furthermore, the A–E bond strength in the complexes becomes weaker with stronger π-back-donation interactions. Finally, W@Au₁₂CO has the largest HOMO–LUMO gap, making it the most stable in terms of kinetic stability.     

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.     

Gas adsorption on the Zn-, Pd- and Os-doped armchair (5,5) single-walled carbon nanotubes

The adsorption of NO₂, NH₃, H₂O, CO₂ and H₂ gases on the undoped, Zn–, Pd– and Os–doped armchair (5,5) single–walled carbon nanotubes (SWCNTs) were studied using density functional method. The adsorptions of these five gases on the Zn–, Pd– and Os–doped SWCNTs are obviously stronger than on the undoped SWCNT and their adsorption abilities are in the same order: NO₂ > NH₃ > H₂O > CO₂ > H₂. Adsorption energies for all the studied gases on the undoped, Zn–, Pd– and Os–doped SWCNTs computed at the B3LYP/LanL2DZ level are reported.     

A Simple and Sensitive SPRS Method for Trace H2O2 Based on the TiO2+ Complex and Gold Nanoparticles Aggregation Reactions

In the medium of H₂SO₄ and in the presence of TiO²⁺, gold nanoparticles in size of 10 nm exhibited a weak surface plasmon resonance scattering (SPRS) peak at 775 nm. Upon addition of trace H₂O₂, the yellow complex [TiO(H₂O₂)]²⁺ formed that cause the gold nanoparticles aggregations to form bigger gold nanoparticle clusters in size of about 900 nm, and the SPRS intensity at 775 nm (I) enhanced greatly. The enhanced intensity ΔI was linear to the H₂O₂ concentration in the range of 0.025–48.7 μg/mL, with a detection limit of 0.014 μg/mL H₂O₂. This SPRS method was applied to determining H₂O₂ in water samples with satisfactory results.     

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.     

The active site of the [FeFe]-hydrogenase from Desulfovibrio desulfuricans. II. Redox properties, light sensitivity and CO-ligand exchange as observed by infrared spectroscopy

In [FeFe]-hydrogenases, the H cluster (hydrogen-activating cluster) contains a di-iron centre ([2Fe]_H subcluster, a (L)(CO)(CN)Fe(μ-RS₂)(μ-CO)Fe(CysS)(CO)(CN) group) covalently attached to a cubane iron-sulphur cluster ([4Fe-4S]_H subcluster). The Cys-thiol functions as the link between one iron (called Fe1) of the [2Fe]_H subcluster and one iron of the cubane subcluster. The other iron in the [2Fe]_H subcluster is called Fe2. The light sensitivity of the Desulfovibrio desulfuricans enzyme in a variety of states has been studied with infrared (IR) spectroscopy. The aerobic inactive enzyme (H_inact state) and the CO-inhibited active form (H_ox–CO state) were stable in light. Illumination of the H_ox state led to a kind of cannibalization; in some enzyme molecules the H cluster was destroyed and the released CO was captured by the H clusters in other molecules to form the light-stable H_ox–CO state. Illumination of active enzyme under ¹³CO resulted in the complete exchange of the two intrinsic COs bound to Fe2. At cryogenic temperatures, light induced the photodissociation of the extrinsic CO and the bridging CO of the enzyme in the H_ox–CO state. Electrochemical redox titrations showed that the enzyme in the H_inact state converts to the transition state (H_trans) in a reversible one-electron redox step (E _{m, pH 7}=–75 mV). IR spectra demonstrate that the added redox equivalent not only affects the [4Fe-4S]_H subcluster, but also the di-iron centre. Enzyme in the H_trans state reacts with extrinsic CO, which binds to Fe2. The H_trans state converts irreversibly into the H_ox state in a redox-dependent reaction most likely involving two electrons (E _{m, pH 7}=–261 mV). These electrons do not end up on any of the six Fe atoms of the H cluster; the possible destiny of the two redox equivalents is discussed. An additional reversible one-electron redox reaction leads to the H_red state (E _{m, pH 7}=–354 mV), where both Fe atoms of the [2Fe]_H subcluster have the same formal oxidation state. The possible oxidation states of Fe1 and Fe2 in the various enzyme states are discussed. Low redox potentials (below –500 mV) lead to destruction of the [2Fe]_H subcluster.     

Metal cluster topology. 2. Gold clusters

Previously developed methods for the treatment of polyhedral boranes, carboranes, and metal clusters are extended to the treatment of gold clusters, which present a variety of new problems. In most cases gold atoms in such cluster compounds do not employ the usual 9-orbital sp³d⁵ spherical bonding orbital manifold. Instead almost all non-tetrahedral gold clusters consist of a center gold atom surrounded by a puckered polygonal belt of peripheral gold atoms generally with one or more additional peripheral gold atoms in distal positions above and/or below the belt. The peripheral gold atoms in such clusters use a 7-orbital spd⁵ cylindrical bonding orbital manifold, but their residual two orthogonal anti- bonding p orbitals can receive electron density from the filled d orbitals of adjacent peripheral gold atoms through dσ → pσ^* and/or dπ → pπ^* backbonding leading to bonding distances between adjacent peripheral gold atoms. Centered gold clusters can be classified into either spherical or toroidal clusters depending upon whether the center gold atom uses a 9-orbital sp³d⁵ spherical bonding orbital manifold or an 8-orbital sp²d⁵ toroidal bonding orbital manifold, respectively. The topology of the core bonding in gold clusters is generally not that of the K_n complete graph found in other clusters but instead mimics the topology of the polyhedron formed by the surface atoms. This apparently is a consequence of the poor lateral overlap of the cylindrical spd⁵ manifolds of the peripheral gold atoms. Examples of non-centered gold clusters treated in this paper include the squashed pentagonal bipyramidal Au₇(PPh₃)₇⁺ and the edge-fused bitetrahedral (Ph₃P)₄Au₆[Co(CO)₄]₂ which may be regarded as a ‘perauraethylene’ in which the six cluster gold atoms correspond to the six atoms of ethylene including a double bond between the two gold atoms corresponding to the two ethylene carbon atoms.     

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.