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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Structures and stabilities of ScBn (n = 1–12) clusters: an ab initio investigation

The geometries, stabilities, and electronic properties of ScB_n (n?=?1–12) clusters have been systematically investigated by using density functional theory B3LYP method and coupled–cluster theory CCSD(T) method. It is found that the ground state isomers of ScB_n have planar or quasi–planar structure when n?≤?6, which can be viewed as a B atom of the corresponding B_n+1 cluster is substituted by a Sc atom. From n?≥?7, the ground state isomers favor nest–like structure, in which the Sc atom sits on a nest–like B_n cluster. The calculated second–order differences of energies manifest that the magic numbers of stability are n?=?3, 7, 8, 9 and 11 for the ScB _n clusters. Further analysis indicates that the ScB₇ cluster with C _6v symmetry represents the outstanding stable ScB_n cluster, as confirmed by its electronic structure and molecular orbitals.     

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.     

Nucleation and mobility model of Ag<Subscript>n</Subscript> clusters adsorbed on perfect and oxygen vacancy MgO surfaces

The structures and energy properties for Ag_n (n = 1-8) metal clusters adsorbed on the perfect and oxygen vacancy MgO surfaces have been studied by using the DFT/UB3LYP method with an embedded cluster model. The nucleation and mobility model for the Ag_n (n = 1-8) clusters on the perfect and oxygen vacancy MgO(100) surfaces was investigated. The results show that the Ag atoms locate initially at the surface oxygen vacancy sites; then, with the growth of Ag cluster sizes, the large Ag clusters move possibly out of the vacancy sites by a rolling model, and diffuse on the MgO surface under a certain temperature condition. The relative energies needed for moving out of the oxygen vacancy region for the adsorbed Ag_n clusters with the rolling model have been predicted. The even-odd oscillation behaviors for the cohesive energies, nucleation energies, first ionization potentials and HOMO-LUMO gaps of the adsorbed Ag_n clusters with the variation of cluster sizes have also been discussed.     

A first-principles study of Ni<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>Pd<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (n = 1 − 5) clusters

A first-principle investigation of structures and properties of Ni _n Pd _n (n=1-5) clusters is presented. For this study, the linear combination of Gaussian-type orbitals auxiliary density functional theory (LCGTO-ADFT) method has been employed. In order to determine the lowest energy structures, several isomers in different spin multiplicities were studied, for each cluster size. Initial structures, for which successive geometry optimization was computed without any constrain, were taken along Born–Oppenheimer molecular dynamics (BOMD) trajectories. To discriminate between minima and transition state structures, harmonic frequency analyses were performed at the optimized structures. Ground state structures, bond lengths, harmonic frequencies, dissociation energy, ionization potential, electron affinity and spin density plots are presented. This work demonstrates, that the Pd atoms prefer to allocate on the surface of the cluster structures whose core is formed by the 3d TM atoms type. Moreover, it has been observed that the ground-state structure spin multiplicity increases as the system size grows. The results of this study contribute to gain insight into how structures and energy properties change with cluster size in bimetallic Pd-based alloys.     

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.     

Crossover of a high-spin (S=7/2, 3/2) to a low-spin (S=1/2) iron-selenium cluster in FA and FB of photosystem I on rebinding of PsaC onto P700-FX cores

 PsaC is a tightly bound ferredoxin in the Photosystem I (PS I) reaction center which contains two [4Fe-4S] clusters named F_A and F_B. We recently proposed that the mixed-ligand F_B cluster in C14D_PsaC and the mixed-ligand F_A cluster in C51D_PsaC exist in a spin state of S=3/2, and that a spin state crossover to S=1/2 occurs when the PsaC mutants are rebound onto P700-F_X cores. Since EPR signals from a highly rhombic S=3/2 spin state can be difficult to study, wild-type PsaC was reconstituted with iron and selenium to introduce an easily detected S=7/2 spin state similar to that shown for Clostridial ferredoxin. When the unbound [4Fe-4Se] PsaC was chemically reduced, a sharp derivative resonance was found at g=5.171 attributed to the excited ±3/2 doublet from an S=7/2 spin multiplet. An additional peak was found at g=5.616 attributed to the superimposed ±1/2 and ±3/2 doublets from a highly rhombic S=3/2 spin multiplet, and an axial set of resonances found around g=2.0 attributed, in part, to a classical S=1/2 spin state. When the [4Fe-4Se] PsaC was rebound onto P700-F_X cores, the spin population derived from the S=7/2 and 3/2 spin states was negligible. Illumination of the rebuilt PS I complex at 15 K resulted in two rhombic sets of resonances, one with g values of 2.043, 1.941 and 1.854, diagnostic of F_A, and the other with g values of 2.067, 1.941 and 1.878, diagnostic of F_B. Chemical reduction with sodium dithionite at pH 10.5 or photoaccumulation by freezing during illumination resulted in a set of resonances with g values of 2.046, 1.938, 1.920 and 1.883, characteristic of a spin-coupled F_A ^–/F_B ^– pair. The spin state crossover in this iron chalcogenide cluster is the first known to be induced by protein-protein association and reinforces the hypothesis that an S=3/2 to 1/2 crossover occurs in the PS I-rebound mutants C14D_PsaC and C51D_PsaC. Received: 6 August 1996 / Accepted: 28 December 1996     

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.     

Theoretical study of crown ethers with incorporated azobenzene moiety

A series of crown ethers containing the azobenzene moiety incorporated into crowns of various sizes [Cr(O₆)_, Cr(O₇) and Cr(O₈)] and their corresponding alkali metal cation (Li⁺, Na⁺, K⁺, Rb⁺) complexes have been studied theoretically. The density functional theory (DFT) method was employed to elucidate the stereochemical structural natures and thermodynamic properties of all of the target molecules at the B3LYP/6-31 G(d) and LANL2DZ level for the cation Rb⁺. The fully optimized geometries had real frequencies, thus indicating their minimum-energy status. In addition, the bond lengths between the metal cation and oxygen atoms, atomic torsion angles and thermodynamic energies for complexes were studied. Natural bond orbital (NBO) analysis was used to explore the origin of the internal forces and the intermolecular interactions for the metal complexes. The calculated results show that the most significant interaction is that between the lone pair electrons of electron-donating oxygens in the cis-forms of azobenzene crown ethers (cis-ACEs) and the LP* (1-center valence antibond lone pair) orbitals of the alkali-metal cations (Li⁺, Na⁺, K⁺ and Rb⁺). The electronic spectra for the cis-ACEs [cis-Cr(O₆), cis-Cr(O₇) and cis-Cr(O₈)] are obtained by the time-dependent density functional theory (TDDFT) at the B3LYP/6-31 G(d) level. The spectra of the cis-isomers show broad π → π* (S₀ → S₂) absorption bands at 310–340 nm but weaker n → π* (S₀ → S₁) bands at 480–490 nm. The calculated results are in good agreement with the experimental results.     

A MP2 and DFT study of the aromatic character of polyphosphaphospholes. Is the pyramidality the only factor to take into consideration?

A comprehensive MP2/6-311 + G(d,p) and B3LYP/6-311 + G(d,p) study of the aromatic character of phospholes, P _n (CH)_4-n PH with n = 0-4 was conducted. For this purpose, the structures for these compounds were optimized at both theoretical levels and different magnetic properties (magnetic susceptibility anisotropy, χ_anis, and the nucleus-independent chemical shifts, NICS) were evaluated. For comparison, these magnetic properties were also calculated in the optimized structures with planarity constraints. We have also applied the ACID (anisotropy of the current-induced density) method in this analysis. The main conclusions are the aromatic character of these compounds, the relationship between aromaticity and planarity and the importance of other factors in this aromaticity.     

Investigation of exchange couplings in [Fe3S4]+ clusters by electron spin-lattice relaxation

3 S₄]⁺, S=1/2, composed of three, antiferromagnetically coupled high-spin ferric ions) by continuous wave (CW) and pulsed EPR techniques: Azotobacter vinelandii ferredoxin I, Desulfovibrio gigas ferredoxin II, and the 3Fe forms of Pyrococcus furiosus ferredoxin and aconitase. The 35 GHz (Q-band) CW EPR signals are simulated to yield experimental g tensors, which either had not been reported, or had been reported only at X-band microwave frequency. Pulsed X- and Q-band EPR techniques are used to determine electron spin-lattice (T ₁, longitudinal) relaxation times at several positions on the samples' EPR envelope over the temperature range 2–4.2 K. The T ₁ values vary sharply across the EPR envelope, a reflection of the fact that the envelope results from a distribution in cluster properties, as seen earlier as a distribution in g ₃ values and in ⁵⁷ Fe hyperfine interactions, as detected by electron nuclear double resonance spectroscopy. The temperature dependence of 1/T ₁ is analyzed in terms of the Orbach mechanism, with relaxation dominated by resonant two-phonon transitions to a doublet excited state at ∼20 cm⁻¹ above the doublet ground state for all four of these 3Fe proteins. The experimental EPR data are combined with previously reported ⁵⁷Fe hyperfine data to determine electronic spin exchange-coupling within the clusters, following the model of Kent et al. Their model defines the coupling parameters as follows: J ₁₃=J, J ₁₂=J(1+ε′), J ₂₃=J(1+ε), where J _ij is the isotropic exchange coupling between ferric ions i and j, and ε and ε′ are measures of coupling inequivalence. We have extended their theory to include the effects of ε′≠0 and thus derived an exact expression for the energy of the doublet excited state for any ε, ε′. This excited state energy corresponds roughly to ε J and is in the range 5–10 cm⁻¹ for each of these four 3Fe proteins. This magnitude of the product ε J, determined by our time-domain relaxation studies in the temperature range 2–4 K, is the same as that obtained from three other distinct types of study: CW EPR studies of spin relaxation in the range 5.5–50 K, NMR studies in the range 293–303 K, and static susceptibility measurements in the range 1.8–200 K. We suggest that an apparent disagreement as to the individual values of J and ε be resolved in favor of the values obtained by susceptibility and NMR (J≳200 cm⁻¹ and ε≳0.02 cm⁻¹ ), as opposed to a smaller J and larger ε as suggested in CW EPR studies. However, we note that this resolution casts doubt on the accepted theoretical model for describing the distribution in magnetic properties of 3Fe clusters. Received: 23 December 1999 / Accepted: 8 March 2000