Geometric and energetic properties of Al-doped Sin (n = 2–21) clusters: FP-LMTO-MD calculations

We have investigated the effect of aluminum impurity atoms on the geometric structures and stabilities of neutral and ionic Si_n (n = 2–21) clusters in detail by using full-potential linear-muffin-tin-orbital molecular-dynamics (FP-LMTO-MD) method. Our calculations suggest that most of the ground state structures for neutral and ionic Si_nAl (n = 1–20) clusters can be obtained by substituting one Si atom of their corresponding Si clusters with an Al atom. The neutral Si_n–1Al clusters with one Al atom have similar geometrical configurations to those of the pure Si_n clusters except for local structural distortion. But one Al impurity atom probably reverses the energy ordering of two isomers with small difference. Although, an Al heteroatom reduces the average binding energies for the mixed clusters, it would improve the bond strength between Si atoms in some mixed clusters. Our calculations also suggest that most of the ionic Si_n–1Al clusters adopt the same geometrical configurations as their neutral clusters. But for one selected mixed cluster, the charged structures probably have different energy ordering from the neutral clusters. The anionic Si_n–1Al⁻ clusters, which are isoelectronic to their corresponding pure Si_n clusters, show similar magic behavior.     

Computational studies of stable hexanuclear CulAgmAun (l + m + n = 6; l,m, n > 0) clusters

A DFT study was carried out on the ground state structures of ternary Cu_lAg_mAu_n (l + m + n = 6) clusters, with the aim of investigating changes of thermal and kinetic stabilities as an effect of composition, as well as the composition dependence of the electrostatic potential, of stable planar structures. DFT optimizations were performed using the PBE functional and the SDD basis set. All the optimized structures adopt planar geometries with bent triangular structures. Calculated binding energy values are in the range 1.5–1.9 eV/atom, which shows their thermal stability. The predicted HOMO‐LUMO energy gap values are in the semiconductor region, providing a qualitative indication of a moderate kinetic stability. NBO analyses indicate the existence of two mechanisms promoting planar structural stability, one due to bonding‐antibonding orbital interaction, and the other one due to the well‐known spd hybridization. Wiberg indices were obtained showing interatomic bonding. Electrostatic potential calculations show the existence of nucleophilic attack regions preferentially around silver and copper atoms located at the vertices while electrophilic attack regions are found in the vicinity of gold atoms over the cluster plane. Apparently, charge transfer occurs toward gold from silver and copper atoms when the concentration is favorable in the proximity of gold atoms. In particular, if the small ternary clusters discussed here contain only one gold atom, then a high electron density is observed at the site of this gold atom. © 2016 Wiley Periodicals, Inc.     

Potential energy surfaces for HenNe+ ions: ab initio and diatomics-in-molecule results

The potential energy surface of He2Ne+ has been reinvestigated using a combination of ab initio and diatomics-in-molecule (DIM) calculations. In contrast to the reports of two recent studies the ion is found to have an asymmetric linear He-Ne-He structure, with no barrier to formation from the separated atoms on the ground-state surface. The He-Ne+ bond lengths at the potential minimum are 1.51 and 1.81 A, and the total bonding energy is 0.717 eV. Comparing the He2Ne+ energy to that of HeNe+, the bonding energy for the second helium atom is 0.06 eV, about 10% of that of the first He atom. The saddle point between the two equivalent minima is a symmetric structure, 0.0074 eV above the potential minimum. A symmetric geometry becomes the overall potential minimum if the 2s hole on the Ne is excluded from the reference states of a multireference configuration interaction calculation. A DIM potential was created for the HenNe+ family of ions. The DIM potential is consistent with the asymmetric He2Ne+ ion serving as a core; it predicts a slightly more asymmetric geometry than the ab initio results. Additional helium atoms form five-membered rings around the bonds of the core ion to fill the first shell and then add to the ends of the cluster. The asymmetric core ion and the highly compact structure help to account for the lack of apparent shell structure in the mass spectrometry of HenNe+ clusters. Finally, we recommend that the value De=0.63+/-0.04 eV be adopted for the ground state of HeNe+.     

Exchange interaction energy between two one-active electron atoms at large distances

Developed formulas for the exchange interaction energy between two neutral one-active electron atoms interacting at large distances R are presented in terms of known basic integrals obtained from an asymptotic method for the alkali dimers M₂ dissociating to M(ns) + M(ns), M(n′l) + M(n′l), l = 0, …, 3 and M (np) + M(np). Detailed illustrative numerical results are displayed for the molecular states of Na₂ dissociating to the limit Na(3s) + Na(3p). Comparisons with very accurate ab initio results as well as with some available experimental data show that accurate potential energy curves for these excited states may be obtained in a very large range of internuclear distances by connecting ab initio curves for small and intermediate values of R with long-range curves obtained as the sum of usual multipolar Coulombic energy and asymptotic exchange energy.     

(BN)n(n≤12)团簇的结构及成键性质

利用遗传算法和Gastreich提出的经验势函数研究了(BN)_n(n≤12)团簇的可能稳定结构, 并对能量较低的异构体在HF/6-31G(d)水平进行优化, 得到了(BN)_n(n≤12)团簇的线状、蒲扇形、单环、双环、三环和笼状结构, 讨论了各种结构的特征及相对稳定性. 分析了BN团簇中原子的成键性质, 在单环结构中, N原子以sp2杂化成键, B原子以sp杂化成键, 而在节点处B原子以sp2杂化成键. (BN)6是唯一没有张力的单环结构.     

A new magic titanium-doped gold cluster and orientation dependent cluster-cluster interaction

The stability and structures of titanium-doped gold clusters Au(n)Ti (n=2-16) are studied by the relativistic all-electron density-functional calculations. The most stable structures for Au(n)Ti clusters with n=2-7 are found to be planar. A structural transition of Au(n)Ti clusters from two-dimensional to three-dimensional geometry occurs at n=8, while the Au(n)Ti (n=12-16) prefer a gold cage structure with Ti atom locating at the center. Binding energy and second-order energy differences indicate that the Au(14)Ti has a significantly higher stability than its neighbors. A high ionization potential, low electron affinity, and large energy gap being the typical characters of a magic cluster are found for the Au(14)Ti. For cluster-cluster interaction between magic transition-metal-doped gold clusters, calculations were performed for cluster dimers, in which the clusters have an icosahedral or nonicosahedral structure. It is concluded that both electronic shell effect and relative orientation of clusters are responsible for the cluster-cluster interaction.     

The ‘triplet-excited region’ in linear polyenes: Real or artifactual?

The geometries for the planar T₁ states of linear polyenes C_nH_n+2 (n=8, 10, 12, 14, 16, 18, 20, and 22) were optimized by ab initio SCI calculations. It was found that the bond alternation which existed in the S₀ state disappears only in the central region of the polyene chain. This is quite similar to the ‘triplet-excited region’ which was observed in PPP SDCI calculations for decapentaene (n=10), tetradecaheptaene (n=14), octadecanonaene (n=18), and docosaundecaene (n=22) (M. Kuki, Y. Koyama, N. Nagae, J. Phys. Chem. 95 (1991) 7171). However, CASSCF calculations performed for octatetraene (n=8) gave considerably different geometries from the SCI geometries. The reason for this is discussed and we conclude that the appearance of the ‘triplet-excited region’ in SCI and SDCI calculations is artifactual.     

吸附O的Cu(110)c(2×1)表面原子结构和电子态

采用第一性原理的密度泛函理论方法计算了清洁Cu(110)表面和吸附O原子的Cu(110) c(2×1)表面的原子结构, 结构弛豫和电子结构, 得到了各种表面结构参数. 分别计算了O原子在Cu(110)表面三个可能吸附位置吸附后的能量, 并给出了能量最低的吸附位置上各层原子的弛豫特性和态密度. 结果表明O吸附后的Cu(110)表面有附加列(added-row)再构的特性, O原子吸附在最表层铜原子上方, 与衬底Cu原子的垂直距离为0.016 nm, 以氧分子为能量基准的吸附能为－1.94 eV; 同时由于Cu 3d- O 2p态的杂化作用使得低于费米能级5.5~6.0 eV的范围内出现了局域的表面态. 计算得到清洁的和氧吸附的Cu(110)表面的功函数分别为4.51 eV和4.68 eV. 电子态密度的结果表明：在Cu(110) c(2×1) 表面O吸附的结构下, 吸附O原子和金属衬底之间的结合主要是由于最表层Cu原子3d态和O原子2p态的相互作用.     

Potential energy surfaces of an adenine-thymine base pair and its methylated analogue in the presence of one and two water molecules: molecular mechanics and correlated ab initio study

Potential energy surfaces of monohydrated and dihydrated adenine-thymine and 9-methyladenine-1-methylthymine base pairs were examined by the molecular dynamics/quenching technique using the Cornell et al. force field (J. Am. Chem. Soc. 1995, 117, 5179). Long runs of molecular dynamics/quenching calculations allowed us to evaluate the free energy surface. The most stable and populated structures found were fully reoptimized at the correlated ab initio level employing the resolution of identity M?ller-Plesset method. A systematic study of the base pairs' microhydration using both the empirical and the high-level correlated ab initio approaches is presented for the first time. We show that the occurrence of water molecules and their gradually increasing number as well as the methylation of the bases favor stacked structures over the planar hydrogen-bonded ones. These results based on the correlated ab initio calculations are in the excellent agreement with data obtained from our previous empirical potential molecular dynamics study (Kabelác et al. Chem.-Eur. J. 2001, 7, 2067).     

Density Functional Theory Study of Pd Aggregation on a Pyridine-Terminated Self-Assembled Monolayer

By using density functional theory calculations, the initial steps towards Pd metal cluster formation on a pyridine-terminated self-assembled monolayer (SAM) consisting of 3-(4-(pyridine-4-yl)phenyl)propane-1-thiol on an Au(1 1 1) surface are investigated. Theoretical modelling allows the investigation of structural details of the SAM surface and the metal/SAM interface at the atomic level, which is essential for elucidating the nature of Pd–SAM and Pd–Pd interactions at the liquid/solid interface and gaining insight into the mechanism of metal nucleation in the initial stage of electrodeposition. The structural flexibility of SAM molecules was studied first and the most stable conformation was identified, planar molecules in a herringbone packing, as the model for Pd adsorption. Two binding sites are found for Pd atoms on the pyridine end group of the SAM. The strong interaction between Pd atoms and pyridines illustrates the importance of SAM functionalisation in the metal nucleation process. Consistent with an energetic driving force of approximately −0.3 eV per Pd atom towards Pd aggregation suggested by static calculations, a spontaneous Pd dimerisation is observed in ab initio molecular dynamic studies of the system. Nudged elastic band calculations suggest a potential route with a low energy barrier of 0.10 eV for the Pd atom diffusion and then dimerisation on top of the SAM layer.     

A molecular level study of the aqueous microsolvation of acetylene

We present an analysis of the structural, energetic and spectral features associated with the different hydrogen bonded networks found in the first few acetylene–water clusters AW_n (n=1–4) from first principles calculations. Contrary to the predictions of an empirical interaction potential, acetylene is incorporated into a hydrogen bonded ring when it clusters with two or three water molecules. This structural pattern changes for n=4 with the formation of a water tetramer interacting with acetylene. This structural transition from n=3 to 4 is spectroscopically manifested by a qualitative change in the appearance of the infrared spectra of the corresponding global minima.     

Geometry and stability of BenCm (n=1-10; m=1, 2, ..., to 11-n) clusters

Density functional theory B3PW91/6-31+G* calculations on BenCm (n=1-10; m=1, 2, ..., to 11-n) clusters have been carried out to examine the effect of cluster size, relative composition, binding energy per atom, HOMO-LUMO gap, vertical ionization potential, and electron affinity on their relative stabilities. The most stable planar cyclic conformations of these clusters always show at least a set of two carbon atoms between two beryllium atoms, while structures where beryllium atoms cluster together, or allow the intercalation of one carbon atom between two of them, generally seem to be the least stable ones. Clusters containing 1, 2, and 3 beryllium atoms (Be2C8, Be3C6, Be2C6, BeC6, Be2C4, BeC4, Be2C2, and BeC2) are identified as clusters of "magic numbers" in terms of their high binding energy per atom, high HOMO-LUMO gap, vertical ionization potential, and second difference in energy per beryllium atom.     

An ab initio study on the vibrational and electronic spectra of the molybdenum–sulfur clusters with Mo2OnS4−n(n=0–4) core

Using the ab initio method, the vibrational and electronic spectra of binuclear molybdenum clusters which contain Mo₂O_nS_4−n(n=0–4) core were investigated. The main absorption bands in the IR spectra of these clusters are assigned and compared with each other, especially for the case of the trans isomers. The electronic spectra were studied by performing the CIS calculations. The ground state and the first excited state of the clusters were discussed by using the natural bond orbital method. It is shown that the band corresponding to the longest wavelength can be assigned to three kinds of transition types. Two transitions, σ(Mo–Mo)→π*(Mo–X_t)(X=S,O) and σ(Mo–Mo)→σ*(Mo–Mo), can be seen in most cases.     

Electronically excited states and visible region photodissociation spectroscopy of Au(m)(+) . Ar(n) clusters (m=7-9): molecular dimensionality transition?

Photodissociation spectra were determined for Au(m)(+) . Ar(n) (m=7; n=0-3 and m=8,9; n=0,1) in the photon energy range of 2.14-3.02 eV. Experimental data were compared with predictions of dipole allowed transitions using time-dependent density functional theory (TDDFT) as applied to cluster structures from both DFT (B3-LYP functional) and ab initio calculations at the MP2 level. Argon adduct formation does not significantly perturb the bare metal cluster core structure, but it does change the metal cluster spectrum for highly symmetric cluster structures. The photodissociation spectra are consistent with a transition from planar to three-dimensional gold cluster core geometries between m=7 and m=8 for both n=0 and 1. TDDFT predictions for favored isomers describe experimental absorption features to within +/-0.25 eV. We also discuss size-dependent trends in TDDFT transition energies for the lowest energy two- and three-dimensional structures of Au(m)(+)(m=3-9).     

Stability and structure of singly-charged argon clusters Ar n + ,n=3–27. A Monte-Carlo simulation

Monte-Carlo calculations have been performed for positively charged argon clusters in the temperature range between 10 K and 40 K using two different models (one with a dimer ion core, the other one with a trimer ion). The argon-argon interaction potential stems from empirical data, the ion-neutral atoms potential is determined by ab initio MRD-CI calculations. Special stability is found for clusters sizesn=13, 19, 23 and 25/26 atoms using the ‘trimeric core model’ and for those withn=14,n=17,n=20 using the ‘dimeric core model’. The geometrical structure of the clusters is given and the construction principles are discussed in light of the interactions among neutral argon atoms and the ion-neutral atoms interaction.     

平面五配位硅、 锗XBe5H6(X=Si,Ge)团簇

采用密度泛函理论PBE0方法, 在aug-cc-pVTZ水平上理论预测了含平面五配位硅和锗原子的XBe₅H₆ (X=Si, Ge)团簇. 势能面系统搜索及高精度量化计算表明, 它们均为全局极小结构. XBe₅H₆(X=Si, Ge)团簇整体呈完美的扇形结构: Si/Ge原子被5个金属Be原子配位; 4个H原子以桥基方式与Be原子相键连, 剩余的2个 H原子以端基方式与两端的Be原子成键. 化学键分析表明, XBe₅H₆(X=Si, Ge) 团簇中XBe₅单元具有完全离域的1个π及3个σ键, 外围铍氢间形成4个Be—H—Be 三中心二电子(3c-2e)键及2个定域的Be—H键. XBe₅单元上离域的2π及6σ电子赋予体系π和σ双重芳香性, 并使Si/Ge原子满足八隅律（或八电子规则）. 能量分解-化学价自然轨道分析揭示, Si/Ge和Be₅H₆之间主要为电子共享键.     

Thorium encapsulated caged clusters of germanium: Th@Ge(n), n = 16, 18, and 20

We report from ab initio calculations that thorium encapsulation can be used to stabilize highly symmetric cages of germanium with 16 and 20 atoms. The lowest energy structures of these clusters are different from the recently found silicon fullerenes and are similar to clusters found in bulk metallic alloys. The binding energies of these clusters are higher compared with the values for the elemental germanium clusters of comparable sizes, and this suggests a strong possibility of their experimental realization in large quantities. Also, Th@Ge(16) has a large highest occupied-lowest unoccupied molecular orbital (HOMO-LUMO) gap of 1.72 eV that makes it interesting for optoelectronic applications.     

Ab initio theoretical calculations of the electronic excitation energies of small water clusters

A direct ab initio molecular dynamics method has been applied to a water monomer and water clusters (H(2)O)(n) (n = 1-3) to elucidate the effects of zero-point energy (ZPE) vibration on the absorption spectra of water clusters. Static ab initio calculations without ZPE showed that the first electronic transitions of (H(2)O)(n), (1)B(1)←(1)A(1), are blue-shifted as a function of cluster size (n): 7.38 eV (n = 1), 7.58 eV (n = 2) and 8.01 eV (n = 3). The inclusion of the ZPE vibration strongly affects the excitation energies of a water dimer, and a long red-tail appears in the range of 6.42-6.90 eV due to the structural flexibility of a water dimer. The ultraviolet photodissociation of water clusters and water ice surfaces is relevant to these results.     

Transition between icosahedral and cuboctahedral nanoclusters of lead

We have used ab initio methods to study the possible transition between icosahedral (ico) and cuboctahedral (fcc) structures in lead nanoclusters of sizes up to 309 atoms. Spontaneous fcc-to-ico transition in Pb(13) was observed in the ab initio molecular dynamics (MD) simulations at various temperatures. The transition path can be described predominantly by an angular variable s, which can, generally be applied to the similar transitions in clusters of larger sizes and was observed to follow the Mackay model. We have calculated the two-dimensional energy surface that describes the transition in Pb(13) and found a barrierless fcc-to-ico transition path, which is consistent with the observed spontaneous transition in the ab initio MD simulations. The atomic displacements in the transition were identified as one of the vibrational eigenmodes of these two Pb(13) clusters. For clusters of larger sizes (Pb(n), where n = 55, 147, and 309), the possible transitions following similar paths were determined not to be barrierless and the sizes of the barriers were determined by the ab initio elastic band method.     

Water monomer interaction with gold nanoclusters from van der Waals density functional theory

We investigate the interaction between water molecules and gold nanoclusters Au(n) through a systematic density functional theory study within both the generalized gradient approximation and the nonlocal van der Waals (vdW) density functional theory. Both planar (n = 6-12) and three-dimensional (3D) clusters (n = 17-20) are studied. We find that applying vdW density functional theory leads to an increase in the Au-Au bond length and a decrease in the cohesive energy for all clusters studied. We classify water adsorption on nanoclusters according to the corner, edge, and surface adsorption geometries. In both corner and edge adsorptions, water molecule approaches the cluster through the O atom. For planar clusters, surface adsorption occurs in a O-up/H-down geometry with water plane oriented nearly perpendicular to the cluster. For 3D clusters, water instead favors a near-flat surface adsorption geometry with the water O atom sitting nearly atop a surface Au atom, in agreement with previous study on bulk surfaces. Including vdW interaction increases the adsorption energy for the weak surface adsorption but reduces the adsorption energy for the strong corner adsorption due to increased water-cluster bond length. By analyzing the adsorption induced charge rearrangement through Bader's charge partitioning and electron density difference and the orbital interaction through the projected density of states, we conclude that the bonding between water and gold nanocluster is determined by an interplay between electrostatic interaction and covalent interaction involving both the water lone-pair and in-plane orbitals and the gold 5d and 6s orbitals. Including vdW interaction does not change qualitatively the physical picture but does change quantitatively the adsorption structure due to the fluxionality of gold nanoclusters.