Structural and electronic properties of stable Aun (n = 2–13) clusters: A density functional study

All-electron scalar relativistic calculations have been performed to investigate the electronic structures of neutral gold clusters (Au_n, n = 2–13) in the gas phase using density functional theory with the generalized gradient approximation. Full geometry optimizations of topologically different clusters and clusters belonging to different symmetry groups have been carried out. Binding energies, ionization potentials, electron affinities, and chemical hardness values are calculated and they are found to be comparable with the available experimental and theoretical results. The most stable structure of each of the cluster has a two-dimensional planar configuration. A three dimensional distorted Y shaped structure (4b) for Au₄, a tri-capped triangle (6b), a chair (6f), and a see-saw structure (6j) for Au₆, an eclipsed sandwich structure (7g) for Au₇, a condensed trigonal bipyramid (9e) and a boat shaped structure (9f) for Au₉, a staggered sandwich (11c) and an eclipsed sandwich structure (11d) for Au₁₁, a ladderane structure (12d) for Au₁₂, and a staggered (13d) and a distorted sandwich structure (13e) for Au₁₃ are characterized for the first time in this work.     

Structures, vibrational frequencies, and electron affinities of SF5On/SF5On (n = 1–3)

The molecular structures, vibrational frequencies, and electron affinities of the SF₅O_n/SF₅O_n⁻ (n = 1–3) species have been examined with four hybrid density functional theory (DFT) methods. The basis set used in this work is of double-ζ plus polarization quality with additional diffuse s- and p-type functions, denoted DZP++. The geometries are fully optimized with each DFT method independently. The SF₅O_n (n = 1–3) species should be potential greenhouse gases. The anion SF₅O₂⁻ with C_s symmetry has a ³A″ electronic state, and the neutral SF₅O₃ with ²A″ electronic state has C_s symmetry. The anions SF₅O₂⁻ and SF₅O₃⁻ should be regarded as SF₅⁻·O₂ and SF₅O⁻·O₂ complexes, respectively. Three different types of the neutral–anion energy separation presented in this work are the adiabatic electron affinity (EA_ad), the vertical electron affinity (EA_vert), and the vertical detachment energy (VDE). The EA_ad values predicted by the B3PW91 method are 5.22 (SF₅O), 4.38 (SF₅O₂), and 3.61 eV (SF₅O₃). Compared with the experimental vibrational frequencies, the BHLYP method overestimates the frequencies, and the other three methods underestimate the frequencies. The bond dissociation energies D_e (SF₅O_n → SF₅O_n−m + O_m) for the neutrals SF₅O_n and D_e (SF₅O_n⁻ → SF₅O_n−m⁻ + O_m and SF₅O_n⁻ → SF₅O_n−m + O_m⁻) for the anions SF₅O_n⁻ are reported.     

DFT study on the intermolecular interactions between Aun (n = 2–4) and thymine

Density functional B3LYP method with 6-31++G** basis set is applied to optimize the geometries of the luteolin, water and luteolin–(H₂O)_n complexes. The vibrational frequencies are also studied at the same level to analyze these complexes. We obtained four steady luteolin–H₂O, nine steady luteolin–(H₂O)₂ and ten steady luteolin–(H₂O)₃, respectively. Theories of atoms in molecules (AIM) and natural bond orbital (NBO) are used to investigate the hydrogen bonds involved in all the systems. The interaction energies of all the complexes corrected by basis set superposition error, are within −13.7 to −82.5 kJ/mol. The strong hydrogen bonding mainly contribute to the interaction energies, Natural bond orbital analysis is performed to reveal the origin of the interaction. All calculations also indicate that there are strong hydrogen bonding interactions in luteolin–(H₂O)_n complexes. The OH stretching modes of complexes are red-shifted relative to those of the monomer.     

Theoretical study on the structures and properties of the isomers of Nn(CH)8−nH8 (n = 0–7)

With replacement of N atoms by CH groups in the most stable chain isomer of N8H8, 34 possible isomers of N_n(CH)_8−nH₈ (n = 0–7) have been designed and optimized at the B3LYP/6-311++G** level of theory. The natural bond orbital (NBO) and atoms in molecules (AIM) analysis are carried out to study the bonding nature and relative stabilities of these conformers. G3MP2 method is applied to calculate energies and heats of formation. The results indicate that the hyperconjugation effect from lone pairs of nitrogen atoms to germinal C–N bonds is the major factor which caused the change of the C–N bond length. With the more replacement of nitrogen atoms by CH groups, the heats of formation of the isomers of N_n(CH)_8−nH₈ (n = 0–7) decrease gradually, but the energies increase linearly.     

The distribution pattern of squares on the stability of F4F6-(BN)n (n = 10–22) polyhedrons

To gain an insight into the structures and stability of F₄F₆-(BN)_n polyhedrons with alternation of B and N atoms, a density functional theory study was performed on all isomers of F₄F₆-(BN)_n polyhedrons with n between 10 and 22. The calculation results demonstrate that the lowest energy isomers do not contain B₄₄ bonds (the bonds shared by two squares) and the energies of those isomers containing B₄₄ bonds increase with the number of B₄₄ bonds linearly, indicating that the energetically favored structures of F₄F₆-(BN)_n polyhedrons satisfy the isolated square rule and square adjacency penalty rule. The structural analysis reveals that the stability is determined by the pyramidalization of B and N atoms at the square–square fusion. The binding energy is fitted to the numbers of edges and a model is proposed for predicting the relative stability of these B–N polyhedral molecules.     

Theoretical study on the structures and properties of LiCn, , and (n = 1–10) clusters

The lithium-doped carbon clusters LiC_n, , and (n = 1–10) have been investigated systemically with density functional theory (DFT) method at the B3LYP/6-311+G* level. According to the total energies of different kinds of isomers, the LiC_n, , and (n = 1–10) clusters have Li-terminated linear ground states structures, except for LiC₂, LiC₃, , and (n = 4–6). The incremental binding energies are evaluated to elucidate the stabilities of the clusters with different numbers of carbon atoms for neutral molecules, cations, and anions, respectively. Clear even–odd alternation effects are observed for the stability of the cationic clusters and anionic clusters, while for neutral LiC_n clusters the alternation effect is less pronounced. Similarly, the ionization potentials and electron affinities of LiC_n also express an obvious parity alternation. In addition, the most favorable dissociation channels are acquired according to the fragmentation energies accompanying various pathways.     

Formal chromium–chromium triple bonds and bent rings in the binuclear cycloheptatrienylchromium carbonyls (C7H7)2Cr2(CO)n (n = 6, 5, 4, 3, 2, 1, 0): A density functional theory study

Binuclear cycloheptatrienylchromium carbonyls of the type (C₇H₇)₂Cr₂(CO)_n (n = 6, 5, 4, 3, 2, 1, 0) have been investigated by density functional theory. Energetically competitive structures with fully bonded heptahapto η⁷-C₇H₇ rings are not found for (C₇H₇)₂Cr₂(CO)_n structures having two or more carbonyl groups. This result stands in contrast to the related (C_nH_n)₂M₂(CO)_n (M = Mn, n = 6; M = Fe, n = 5; M = Co, n = 4) systems. Most of the predicted (C₇H₇)₂Cr₂(CO)_n structures have bent trihapto or pentahapto C₇H₇ rings and CrCr distances in the range 2.4–2.5 Å suggesting formal triple bonds. In some cases rearrangement of the heptagonal C₇H₇ ring to a tridentate cyclopropyldivinyl or tridentate bis(carbene)alkyl ligand is observed. In addition structures with CO insertion into the C₇H₇–Cr bond are predicted for (C₇H₇)₂Cr₂(CO)_n (n = 6, 4, 2). The global minima found for the (C₇H₇)₂Cr₂(CO)_n derivatives for n = 6, 5, and 4 are (η⁵-C₇H₇)(OC)₂CrCr(CO)₄(η¹-C₇H₇), (η³-C₇H₇)(OC)₂CrCr(CO)₃(η^2,1- C₇H₇), and (η⁵-C₇H₇)₂Cr₂(CO)₄, respectively. The global minima for (C₇H₇)₂Cr₂(CO)_n (n = 3, 2) have rearranged C₇H₇ groups. Singlet and triplet structures with heptahapto η⁷-C₇H₇ rings are found for the dimetallocenes (η⁷-C₇H₇)₂Cr₂(CO) and (η⁷-C₇H₇)₂Cr₂, with the singlet structures being of much lower energies in both cases.     

Theoretical study of electronic spectra of linear carbon clusters HC2nS (n = 1–5)

In this work we report the structures and stabilities of linear carbon clusters HC_2nS (n = 1–5) in their ground states using the B3LYP density functional. The rotational constants at the optimized geometries give excellent agreement with the experimental and previous theoretical values. The vertical excitation energies of the 2²Π ← X²Π transitions at the CASPT2 level are 3.16, 2.66, 2.05, 1.78, and 1.55 eV, respectively, in good agreement with the corresponding observed values of 3.01, 2.48, 2.10, 1.84, and 1.65 eV. Also, the exponential-decay curves for these vertical excitation energies obtained from experiments and theoretical calculations are illuminated.     

Density functional study of hydrogen adsorption and dissociation on small Pdn (n = 1–7) clusters

Density functional theory has been performed to investigate the interaction of H₂ and Pd_n clusters (n = 1–7). The local minima configurations for different H₂ molecule approach modes towards Pd_n clusters are presented. Our results show that in some cases H₂ is physically adsorbed around Pd atom, and in other cases H₂ is dissociated to be H atoms. Except for PdH2, Pd_n clusters with H atoms dissociatively adsorbed are most stable. For these most stable PdnH2 clusters (n  2), the binding energy of hydrogen atom decreases as the number of Pd atom increases until n = 4, and when n  4, the binding energy almost keeps constant with the H atoms bound sites changing from Pd–Pd bonds to Pd triangle planes. Besides, the adsorption of H₂ on other low-lying isomers of Pd_n clusters is also discussed.     

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.     

Density-functional calculations of MnC(M = Fe, Co, Ni, Cu, n = 1–6) clusters

The structural, energetic and magnetic properties of M_nC(M = Fe, Co, Ni, Cu, n = 1–6) clusters are systematically investigated by density-functional calculations. We found that the ground-state geometrical structures of M_nC clusters are different from those of pure M_n+1 clusters. Fe₄C, Ni₂C and Cu₄C possess relatively higher stabilities. Doping of a C atom enhances the binding energy of M_n clusters, and the binding energies of Fe_n-C, Co_n-C and Ni_n-C are stronger than that of Cu_n-C.     

Parity alternation of interstellar molecules cyanopolyynes HCnN (n = 1–17)

In this paper, we report the design of models for interstellar molecules HC_nN (n = 1–17) by means of the B3LYP density functional method. We performed geometry optimization and calculation on vibrational frequency. We find that the ground-state (G-S) isomers of HC_nN (n = 1–17) are with the N atom located at one end and the H atom at the other end of a C_n chain; they are all linear except for HC₂N which is bent. When n is odd, the C_n chain is polyacetylene-like whereas when n is even, the C_n chain displays a structure that is cumulenic-like in the middle of the C_n chain. It is found that the G-S isomers of odd-n HC_nN (n = 1–17) are more stable than those of even-n ones. The finding is in accord with the relative intensities of HC_nN recorded in laboratory investigations, and in consistent with the results of objects observed in interstellar media. We provide explanations for such a trend of even/odd alternation based on concepts of the highest vibrational frequency, bonding character, electronic configuration, incremental binding energy, nucleus-independent chemical shift, and dissociation channels.     

DFT studies on nonlinear optical properties of neutral nest-shaped heterothiometallic [MOS3Py5Cu3X] (M = Mo, W; X = F, Cl, Br, I) clusters

Theoretical calculations were carried out on some neutral nest-shaped heterothiometallic cluster compounds [MOS₃Py₅Cu₃X] (M = Mo, W; X = F, Cl, Br, I) with the high first static hyperpolarizabilities β values. The geometries of these cluster compounds were optimized by the restricted DFT method at B3LYP level with LanL2DZ base set without any constrains. In order to understand the relationship between the first static hyperpolarizabilities and the compositions of these clusters, the frontier orbital compositions and energy gaps between the HOMO and LUMO orbitals were calculated and analysed. In these clusters the HOMO orbitals are mainly composed of halogen atoms and the first static hyperpolarizability increases from F to I atom. The LUMO orbitals of clusters [MoOS₃Py₅Cu₃X] are comprised of Mo, O and S atoms while the LUMO orbitals of clusters [WOS₃Py₅Cu₃X] composed of W atom and pyridine ring. The energy gaps between the HOMO and LUMO orbitals of the clusters [MoOS₃Py₅Cu₃X] are smaller than those of the clusters [WOS₃Py₅Cu₃X]. As a result the first static hyperpolarizability values of the clusters [MoOS₃Py₅Cu₃X] are higher than those of the clusters [WOS₃Py₅Cu₃X].     

Structures and energies of CnS (1 ≤ n ≤ 20) sulphur carbide clusters

C_nS (1 ≤ n ≤ 20) clusters have been investigated by means of the density functional theory. As a general rule, when 1 ≤ n ≤ 17 the energetically most favorable isomers are found to be the linear arrangement of nuclei (C_∞v) with the sulphur atom at the very end of the carbon chain. The electronic ground state is alternately predicted to be ¹∑⁺ for odd n or ³∑⁻ for even n with a conspicuous odd–even effect in the stability of these clusters. The C₁₈S cluster is predicted to have a S-capped monocyclic structure (¹A₁), but with a low barrier to linearity. On the other hand, C₁₉S and C₂₀S are unambiguously linear in the ¹∑⁺ and ³∑⁻ electronic ground states, respectively.     

IR-photodissociation and photodetachment spectroscopy of Cl · (NH3)x (IR: x = 1–4, PD: x = 1)

Complexes of ammonia molecules and one chloride ion have been studied by photodetachment and IR-photodissociation spectroscopy. For the smallest anionic complex, the stabilisation energy with respect to the bare chloride ion and vibrational frequencies have been determined. Two bands showed a splitting due to rotational branches, which could be represented by simulation. Rotational constants obtained by former ab initio calculations [P.S. Weiser, D.A. Wild, P.P. Wolynec, E.J. Bieske, J. Phys. Chem. A 104 (2000) 2562] are confirmed and rotational constants of a vibrationally excited state are supplied. IR-photodissociation spectra of clusters with up to four ammonia molecules per chloride ion were recorded.     

Theoretical studies of uracil–(H2O)n (n = 1–7) clusters by ab initio and ABEEMσπ/MM fluctuating charge model

Uracil–(H₂O)_n (n = 1–7) clusters were systemically investigated by ab initio methods and the newly constructed ABEEMσπ/MM fluctuating charge model. Water molecules have been gradually placed in an average plane containing uracil. The geometries of 38 uracil–water complexes were obtained using B3LYP/6-311++G** level optimizations, and the energies were determined at the MP2/6-311++G** level with BSSE corrections. The ABEEMσπ/MM potential model gives reasonable properties of these clusters when comparing with the present ab initio data. For interaction energies, the root mean square deviation is 0.96 kcal/mol, and the linear coefficient reaches 0.997. Furthermore, the ABEEMσπ charges changed when H₂O interacted with the uracil molecule, especially at the sites where the hydrogen bond form. These results show that the ABEEMσπ/MM model is fine giving the overall characteristic hydration properties of uracil–water systems in good agreement with the high-level ab initio calculations.     

Electronic spectra of the linear magnesium-containing carbon chains MgC2nH (n = 1–5): A CASPT2 study

Complete active space self-consistent-field (CASSCF) approach has been used for the geometry optimization of the X²Σ⁺ and A²Π electronic states for the linear magnesium-containing carbon chains MgC_2nH (n = 1–5). Multireference second-order perturbation theory (CASPT2) has been used to calculate the vertical excitation energies from the ground to selected seven excited states, as well as the potential energy curves of two ²Σ⁺ and two ²Π electronic states. The studies indicate that the vertical excitation energies of the A²Π ← X²Σ⁺ transition for MgC_2nH (n = 1–5) are 2.837, 2.793, 2.767, 2.714, and 2.669 eV, respectively, showing remarkable linear size dependence. Compared with the previous TD-DFT and RCCSD(T) results, our estimates for MgC_2nH (n = 1–3) are in the best agreement with the available observed data of 2.83, 2.78, and 2.74 eV, respectively. In addition, the dissociation energies in MgC_2nH (n = 1–5) are also been evaluated.     

Density functional theory analysis of CaRgn complexes: (Rg=He, Ne, Ar; n=1–4)

CaRg_n⁺ (Rg=He, Ne, Ar) complexes with n=1–4, are investigated by performing using the B3LYP/6-311+G (3df) density functional theory calculations. The CaHe_n⁺ (n=1–4) complexes are found to be stable. In the case of CaNe_n⁺ and CaAr_n⁺, stable structures and stationary point were found only for n=1 and 2. For n=3 in the C_3V and the D_3h point group as well as for n=4 in the T_d (tetrahedral) point group a saddle point (imaginary frequency) is observed and global minimum could be obtained along the potential energy surface.     

Unsaturation in trinuclear cobalt carbonyl compounds of the type ECo3(CO)n (E = CH,CF, P,As; n = 9, 8, 7, 6) with Co3E tetrahedrane structures

Theoretical studies on the known trinuclear cobalt carbonyl derivatives ECo₃(CO)₉ (E = CH, CF, P, As) predict structures with carbonyl groups bridging each edge of the Co₃ triangle in contrast with experiment where structures with all terminal carbonyl groups are found in all cases. However, the energy differences are predicted to be rather small ranging from 4 ± 2 kcal/mol for FCCo₃(CO)₉ to 10 ± 3 kcal/mol for AsCo₃(CO)₉. The global minima for the unsaturated ECo₃(CO)_n (n = 8, 7, 6) derivatives generally have two (for n = 8) or three (for n = 7 and 6) carbonyl groups bridging the edges of the Co₃ triangle. However, structures with all terminal carbonyl groups are also found in all cases as well as higher energy structures in which one of the carbonyl groups bridges all three cobalt atoms. The fluoromethinyl derivatives FCCo₃(CO)_n (n = 9, 8, 7) are anomalous since their unbridged structures or structures with a carbonyl group bridging all three cobalt atoms are closer in energy to the doubly or triply bridged global minima than is the case for the other ECo₃(CO)_n derivatives.     

Catalytic hydrogenolysis of alkyl halides by sulfido-bridged molybdenum clusters: A density functional study

Density functional theory has been used to explore the mechanism of cleavage of H₂ at a sulfido-bridged molybdenum cluster, CpMo(μ-SH)(μ-S)(μ-S₂CH₂)MoCp. The addition occurs across a single Mo-S bond, and the disruption of the strong Mo-S π bonding in the ground state leads to a very high-lying transition state (+43 kcal mol⁻¹). Once formed, the adsorbed hydrogen migrates over the cluster via a series of hops from metal to sulphur, formally corresponding to a switch from hydridic to protic character. The low barrier (+15 kcal mol⁻¹) for migration leads to facile hydrogenolysis of coordinated substrates.