Density functional study of structural and electronic properties of maximum‐spin n+1Aun−1Ag clusters

The structures and relative stabilities of high‐spin ⁿ⁺¹Au_n?1Ag and ⁿAu_n?1Ag⁺ (n = 2–8) clusters have been studied with density functional calculation. We predicted the existence of a number of previously unknown isomers. Our results revealed that all structures of high‐spin neutral or cationic Au_n?1Ag clusters can be understood as a substitution of an Au atom by an Ag atom in the high‐spin neutral or cationic Au_n clusters. The properties of mixed gold–silver clusters are strongly sized and structural dependence. The high‐spin bimetallic clusters tend to be holding three‐dimensional geometry rather than planar form represented in their low‐spin situations. Silver atom prefers to occupy those peripheral positions until to n = 8 for high‐spin clusters, which is different from its position occupied by light atom in the low‐spin situations. Our theoretical calculations indicated that in various high‐spin Au_n?1Ag neutral and cationic species, ⁵Au₃Ag, ³AuAg and ⁵Au₄Ag⁺ hold high stability, which can be explained by valence bond theory. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Electronic structure and stability of BP clusters: theoretical calculations for (BP)n (n = 2–4)

The geometry, electronic configurations, harmonic vibrational frequencies, and stability of the structural isomers of boron phosphide clusters have been investigated using density functional theory (DFT). CCSD(T) calculations show that the lowest‐energy structures are cyclic (IIt, IVs) with D_nh symmetry for dimers and trimers. The caged structure for B₄P₄ lie higher in energy than the monocyclic structure with D_2d symmetry (VIs). The B–P bond dominates the structures for many isomers, so that one preferred dissociation channel is loss of the BP monomer. The hybridization and chemical bonding in the different structures are also discussed. Comparisons with boron nitride clusters, the ground state structures of B_nP_n (n = 2, 3) clusters are analogous to those of their corresponding B_nN_n (n = 2, 3) counterparts. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Structure and stability for (AlN)_n~+ and (AlN)_n~- (n=1-15) clusters

Using density functional theory (DFT) method with 6-31G* basis set, we have carried out the optimizing calculation of geometry, vibrational frequency and thermodynamical stability for(AIN)n+ and (AIN)n- (n =1-15) clusters. Moreover, their ionic potential (IP) and electron affinity(EA) were discussed. The results show that the electrical charge condition of the cluster has a relatively great impact on the structure of the cluster and with the increase of n, this kind of impactis reduced gradually. There are no AI-AI and N-N bonds in the stable structure of (AIN)n+ or (AIN)n-, and the AI-N bond is the sole bond type. The magic number regularity of (AIN)n+, and (AIN)n- is consistent with that for (AIN)n, indicating that the structure with even n such as 2, 4,6, … is more stable. In addition, (AIN)10 has the maximal ionization power (9.14 eV) and the minimal electron affinity energy (0.19 eV), which manifests that (AIN)10 is more stable than other clusters.     

Quantum chemical exploration of formaldehyde clusters (H2CO)n (n = 2–4)

Global exploration of equilibrium structures and interconversion pathways on the quantum chemical potential energy surface (PES) is performed for (H₂CO)n (n = 2–4) by using the Scaled Hypersphere Search‐Anharmonic Downward Distortion Following (SHS‐ADDF) method. Density functional theoretical (DFT) calculations with empirical dispersion corrections (D3) yielded comparable results for formaldehyde dimer in comparison with recent detailed studies at CCSD(T) levels. Based on DFT‐D3 calculations, trimer and tetramer structures and their stabilities were studied. For tetramer, a highly symmetrical S₄ structure was found as the most stable form in good accordance with experimentally determined tetramer unit in the formaldehyde crystal. © 2018 Wiley Periodicals, Inc.     

Theoretical prediction for the structures of gas phase lithium oxide clusters: (Li2O)n (n = 1–8)

We apply genetic algorithm combining directly with density functional method to search the potential energy surface of lithium‐oxide clusters (Li₂O)_n up to n = 8. In (Li₂O)_n (n = 1–8) clusters, the planar structures are found to be global minimum up to n = 2, and the global minimum structures are all three‐dimensional at n ≥ 3. At n ≥ 4, the tetrahedral unit (TU) is found in most of the stable structures. In the TU, the central Li is bonded with four O atoms in sp³ interactions, which leads to unusual charge transformation, and the probability of the central Li participating in the bonding is higher by adaptive natural density partitioning analysis, so the central Li is in particularly low positive charge. At large cluster size, distortion of structures is viewed, which breaks the symmetry and may make energy higher. The global minimum structures of (Li₂O)₂, (Li₂O)₆, and (Li₂O)₇ clusters are the most stable magic numbers, where the first one is planar and the later both have stable structural units of tetrahedral and C_4v. © 2012 Wiley Periodicals, Inc.     

Theoretical investigation of gas phase ethanol–(water)n (n = 1–5) clusters and comparison with gas phase pure water clusters (water)n (n = 2–6)

Various properties (such as optimal structures, structural parameters, hydrogen bonds, natural bond orbital charge distributions, binding energies, electron densities at hydrogen bond critical points, cooperative effects, and so on) of gas phase ethanol–(water)_n (n = 1–5) clusters with the change in the number of water molecules have been systematically explored at the MP2/aug‐cc‐pVTZ//MP2/6‐311++G(d,p) computational level. The study of optimal structures shows that the most stable ethanol‐water heterodimer is the one where exists one primary hydrogen bond (O? H…O) and one secondary hydrogen bond (C? H …O) simultaneously. The cyclic geometric pattern formed by the primary hydrogen bonds, where all the molecules are proton acceptor and proton donor simultaneously, is the most stable configuration for ethanol–(water)_n (n = 2–4) clusters, and a transition from two‐dimensional cyclic to three‐dimensional structures occurs at n = 5. At the same time, the cluster stability seems to correlate with the number of primary hydrogen bonds, because the secondary hydrogen bond was extremely weaker than the primary hydrogen bond. Furthermore, the comparison of cooperative effects between ethanol–water clusters and gas phase pure water clusters has been analyzed from two aspects. First of all, for the cyclic structure, the cooperative effect in the former is slightly stronger than that of the latter with the increasing of water molecules. Second, for the ethanol–(water)₅ and (water)₆ structure, the cooperative effect in the former is also correspondingly stronger than that of the latter except for the ethanol–(water)₅ book structure. © 2012 Wiley Periodicals, Inc.     

Theoretical investigation of geometry and stability of small lithium‐iodide LinI (n = 2–6) clusters

We present theoretical investigation of the structural characteristics and stabilities of neutral and positively charged Li_nI (n = 2‐6) species. The structural isomers were found by using a randomized algorithm to search for minima structures, followed by B3LYP optimizations; the single‐point RCCSD(T)/cc‐pwCVTZ(‐PP) calculations were performed in order to compute relative energies, binding energies per atom, adiabatic and vertical ionization energies, and dissociation energies. Stability was compared to the pure lithium clusters; there is a typical odd‐even alternation; iodine doped clusters are more stable than pure lithium clusters. Lithium “cage” transfers its valence electron to the iodine atom to form neutral and cationic clusters. An electron departures the lithium cage upon ionization. An important reason for the larger stability of closed‐shell species is the existence of the HOMO 3c/2e natural bond orbitals. © 2013 Wiley Periodicals, Inc.     

Structure and stability of coinage metal fluoride and chloride clusters (MnFn and MnCln,M = Cu,Ag, or Au; n = 1–6)

Calculations in the framework of the density functional theory are performed to study the lowest‐energy isomers of coinage metal fluoride and chloride clusters (M_nF_n, M_nCl_n, M = Cu, Ag, or Au, n = 1–6). For all calculated species starting from the trimers the most stable structures are found to be cyclic arrangements. However, planar rings are favored in the case of metal fluorides whereas metal chlorides prefer nonplanar cycles. Calculated bond lengths and infrared frequencies are compared with the available experimental data. The nature of the bonding, involving both covalent and ionic contributions, is characterized. The stability and the fragmentation are also investigated. Trimers are found to be particularly stable when considering the Gibbs free energies. © 2012 Wiley Periodicals, Inc.     

Far‐Infrared Spectra of Yttrium‐Doped Gold Clusters AunY (n=1–9)

The geometric, spectroscopic, and electronic properties of neutral yttrium‐doped gold clusters Au_nY (n=1–9) are studied by far‐infrared multiple photon dissociation (FIR‐MPD) spectroscopy and quantum chemical calculations. Comparison of the observed and calculated vibrational spectra allows the structures of the isomers present in the molecular beam to be determined. Most of the isomers for which the IR spectra agree best with experiment are calculated to be the energetically most stable ones. Attachment of xenon to the Au_nY cluster can cause changes in the IR spectra, which involve band shifts and band splittings. In some cases symmetry changes, as a result of the attachment of xenon atoms, were also observed. All the Au_nY clusters considered prefer a low spin state. In contrast to pure gold clusters, which exhibit exclusively planar lowest‐energy structures for small sizes, several of the studied species are three‐dimensional. This is particularly the case for Au₄Y and Au₉Y, while for some other sizes (n=5, 8) the 3D structures have an energy similar to that of their 2D counterparts. Several of the lowest‐energy structures are quasi‐2D, that is, slightly distorted from planar shapes. For all the studied species the Y atom prefers high coordination, which is different from other metal dopants in gold clusters.     

Structure and stability of (AlN)n clusters

AIN and Al2N2 have been observed in the record of time-of-flight mass-spectra as positive ions. Associating with density functional theory(DFT) B3LYP method with 6-31G* basis set, we have carried out the optimizing calculations of the geometry, electronic state and vibrational frequency for (AIN)n (n = 1-15) clusters, moreover, discussed the character of the chemical bond and thermodynamical stability and explained the experimental mass spectra. The results show that there do not exist AI-AI and N-N bonds and only exists AI-N bond in the ground state structures of (AIN)n clusters; and the "magical number" regularity of (AIN)n is those whose atom number Is 4, 8, 12,16, 20, etc, all of which are times of four.     

A novel crystal structure of {tris[4‐(1H‐pyrazol‐3‐yl‐κN2)‐3‐azabut‐3‐enyl]amine‐κN}iron(II) bis(tetrafluoridoborate) methanol monosolvate featuring a low‐spin configuration

Mononuclear complexes are good model systems for evaluating the effects of different ligand systems on the magnetic properties of iron(II) centres. A novel crystal structure of the title compound, [Fe(C₁₈H₂₄N₁₀)](BF₄)₂·CH₃OH, with one molecule of methanol per formula unit exhibits a strictly sixfold coordination sphere associated with a low‐spin configuration at the metal centre. The incorporated methanol solvent molecule promotes extended hydrogen‐bonding networks between the tetrafluoridoborate anions and the cationic units. A less constrained crystal structure regarding close contacts between the tetrafluoridoborate anions and the cationic units allows a spin transition which is inhibited in the previously published hydrate of the title compound.     

FeIII in a low‐spin state in caesium bis[3‐ethoxysalicylaldehyde 4‐methylthiosemicarbazonato(2–)‐κ3O2,N1,S]ferrate(III) methanol monosolvate

The synthesis and crystal structure (at 100 K) of the title compound, Cs[Fe(C₁₁H₁₃N₃O₂S₂)₂]·CH₃OH, is reported. The asymmetric unit consists of an octahedral [Fe^III(L)₂]⁻ fragment, where L²⁻ is 3‐ethoxysalicylaldehyde 4‐methylthiosemicarbazonate(2−) {systematic name: [2‐(3‐ethoxy‐2‐oxidobenzylidene)hydrazin‐1‐ylidene](methylamino)methanethiolate}, a caesium cation and a methanol solvent molecule. Each L²⁻ ligand binds through the thiolate S, the imine N and the phenolate O atoms as donors, resulting in an Fe^IIIS₂N₂O₂ chromophore. The O,N,S‐coordinating ligands are orientated in two perpendicular planes, with the O and S atoms in cis positions and the N atoms in trans positions. The Fe^III cation is in the low‐spin state at 100 K.     

配合物[Cu2(bpe)X2] n (bpe =1, 2–trans–(4–pyridyl)ethene, X=Cl, Br, I )的合成、晶体结构及热稳定性研究

以1,2-反式-二（4-吡啶基）乙烯桥连卤化铜分别得到配合物[Cu₂(bpe)Cl ₂] _n (1), [Cu₂(bpe)Br₂] _n (2) 和 [Cu₂(bpe)I₂] _n (3)。通过X-射线单晶衍射法对配合物1的结构进行了研究,晶体学数据：单斜晶系, P 2(1)/c空间群, a = 0.3788(8) nm, b = 1.5059(3) nm, c = 1.0875(2)nm, β = 96.262(4) °, V = 616.5(2)ų, Z = 2, S = 1.002,最终残差因子( I >2 σ ( I )) R ₁ = 0.0288, wR ₂ = 0.0579,对于全部数据 R ₁ = 0.0509, wR ₂ = 0.0615。元素分析及红外光谱分析表明,该类配合物为同晶化合物。另外,通过热重分析对配合物的热稳定性进行了研究。     

The molecular structure of high‐spin (S = ) manganese(II) phthalocyanine in tetrabutylammonium bromido(phthalocyaninato)manganese(II)

The title complex salt, (C₁₆H₃₆N)[MnBr(C₃₂H₁₆N₈)] or (TBA)[Mn^IIBr(Pc)] (TBA is tetrabutylammonium and Pc is phthalocyaninate), has been obtained as single crystals by the diffusion technique and its crystal structure was determined using X‐ray diffraction. The high‐spin (S = ) [Mn^IIBr(Pc)]⁻ macrocycle has a concave conformation, with an average equatorial Mn—N(Pc) bond length of 2.1187 (19) Å, an axial Mn—Br bond length of 2.5493 (7) Å and with the Mn^II cation displaced out of the 24‐atom Pc plane by 0.894 (2) Å. The geometry of the Mn^IIN₄ fragment in [Mn^IIBr(Pc)]⁻ is similar to that of the high‐spin (S = ) manganese(II) tetraphenylporphyrin (TPP) in [Mn^II(1‐MeIm)(TPP)] (1‐MeIm is 1‐methylimidazole).     

Quantum‐chemical study of the spin transition complex [Fe(bt)2(NCS)2] (bt=2,2′‐bithiazoline)

The spin crossover compound [Fe(bt)₂(NCS)₂] has been studied by several density functionals and basis sets. In the calculation, optimized geometries of the compound in the low‐, intermediate‐, and high‐spin states, the vibrational modes and IR spectra, spin splittings energies, excited states, and UV/vis absorption spectra were obtained. © 2012 Wiley Periodicals, Inc.     

Synthesis of Well‐Defined Bicapped Octahedral Iron Clusters [(trenL)2Fe8(PMe2Ph)2]n (n=0, −1)

The synthesis of polynuclear clusters with control over size and cluster geometry remains an unsolved challenge. Herein, we report the synthesis and characterization of open‐shell octairon clusters supported by two heptaamine ligands [o‐H₂NC₆H₄NH(CH₂)₂]₃N (^trenLH₉). The crystal structure of the all‐ferrous species ([^trenL)₂Fe₈(PMe₂Ph)₂] ( 1 ) displays a bicapped octahedral geometry with Fe? Fe distances ranging from 2.4071(6) to 2.8236(5) Å, where the ligand amine units are formally in amine, amide, and imide oxidation states. Several redox states of the octairon cluster are accessible, as ascertained using cyclic voltammetry. The one‐electron‐reduced clusters [M]⁺[(^trenL)₂Fe₈(PMe₂Ph)₂]^? (M=Bu₄N ( 2 a ); (15‐crown‐5)Na(thf) ( 2 b )) were isolated and characterized. Variable‐temperature magnetic susceptibility data indicates that the exchange coupling within the [Fe₈] core is antiferromagnetic which is attenuated upon reduction to the mixed valent anion.     

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

The possible geometrical structures and relative stability of silicon–sulfur clusters (SiS₂) (n=1–6) are explored by means of density functional theory (DFT) quantum chemical calculations. We also compare DFT with second‐order Møller–Plesset (MP2) and Hartree–Fock (HF) methods. The effects of polarization functions, diffuse functions, and electron correlation are included in MP2 and B3LYP quantum chemical calculations, and B3LYP is effective in larger cluster structure optimization, so we can conclude that the DFT approach is useful in establishing trends. The electronic structures and vibrational spectra of the most stable geometrical structures of (SiS₂)_n⁻ are analyzed by B3LYP. As a result, the regularity of the (SiS₂)_n⁻ cluster growing is obtained, and the calculation may predict the formation mechanism of the (SiS₂)_n⁻ cluster. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 280–290, 2001     

DFT studies on TinC2n (n=1–6) clusters

The geometric configurations and electronic structures of the Ti_nC_2n (n=1–6) clusters were studied by using the quantum chemical ab initio density functional theory (DFT) method. Our studies showed that these Ti_nC_2n (n=1–6) could grow gradually to form cyclic clusters through the subunits TiC₂ bonding to each other by C C or Ti C bond. The result could explain the existing experimental fact. The studies might also be helpful to the knowledge of the formation mechanism of the Met‐Cars. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 313–318, 1999