Local analysis and comparative study of the hydrogen bonds in the linear (HCN)n and (HNC)n clusters

B3LYP/6-311+G(2d,p), the density functional theory method of 98 package, is applied to study the hydrogen bonding of a series of linear (HCN)_n and (HNC)_n molecular clusters (for n=1–10). By the localization analysis methods we developed, pair-wised σ type H-bond orders and bond energies are calculated for each pair of the two near-by molecules in both (HCN)_n and (HNC)_n clusters. The calculated results are checked well with the shortening of N–H or C–H distance, the elongation of CH or NH bond distance, and the red shift of stretching frequencies of CH or NH. All pieces of evidence show that the central pair of the two molecules forms the strongest H bond when n of (HCN)_n or (HNC)_n is even, and the two middle pairs form the two strongest H bonds when n is odd. Two terminal pairs of HCN or HNC molecules always form the two weakest H-bonds in each molecular cluster. When comparing molecular cluster energies between (HCN)_n and (HNC)_n for various values of n, the well-known (HCN)_n is found more stable than the related (HNC)_n from energy calculation. However, if outcomes of H-bond local analysis are contrasted, our analysis significantly shows that inter-molecular H-bonds inside of (HNC)_n clusters are much stronger than the corresponding H-bonds in (HCN)_n with the same n. In comparing energy differences between these related clusters per monomer, [E_(HNC)n−E_(HCN)n]/n is found decreasing monotonically as n increases. All pieces of evidence from this theoretical prediction indicate that (HNC)_n with large n is probably constructed by its relative strong H-bonds.     

Theoretical investigation on the adsorption of lithium atom on the Sin cluster (n=2–7)

Ab initio calculations are carried out to study the adsorption of Lithium atom on the Si_n cluster with n ranging from 2 to 7. At the MP2/6-31G(d) level, the structures of the neutral Si_n clusters and the Si_nLi clusters (n=2–7) are optimized. The single-point energy at QCISD/6-311+G(d,p) level for the optimized isomers are further performed. Harmonic vibrational frequency analysis at the MP2/6-31G(d) level is also undertaken to confirm that the optimize geometries are stable. Based on our results, the most favorable sites for Li adsorption on the Si_2–7 clusters are the bridge sites. In addition, the vertical ionization energies of the Si_nLi clusters and the electron affinities of the Si_n clusters are also calculated. The clear parallelism between the vertical ionization energies of Si_nLi and the electron affinities of Si_n is found. This is consistent with the fact that the framework of the Si_n in the Si_nLi cluster is similar to the structure of the corresponding negative ion .     

A density functional study on hydrated clusters of orthoboric acid, B(OH)3(H2O)n (n=1–5)

We have calculated the optimized structures and stabilization energies for hydrated clusters of orthoboric acid molecule, B(OH)₃(H₂O)_n (n=1–5), with a hybrid density functional approach. Although some ion-pair structures are revealed in the case of n=4 and 5 clusters, the most stable structure is found to be a non-proton-transferred form up to n=5 hydrated clusters. The calculated IR spectra of the stable B(OH)₃(H₂O)_n of n=3–5 clusters predict small red shifts of hydrogen-bonded OH frequencies. These geometry and IR results are related to the weak acidity nature of orthoboric acid.     

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.     

Theoretical studies on the BN substituted fullerenes C70−2x(BN)x (x=1–3)—isoelectronic equivalents of C70

The equilibrium structures and relative stabilities of BN-doped fullerenes C_70−2x(BN)_x (x=1–3) have been studied at the AM1 and MNDO level. The most stable isomers of C_70−2x(BN)_x have been found out and their electronic properties have been predicted. The calculation results show that the BN substituted fullerenes C_70−2x(BN)_x have considerable stabilities, though they are less stable than their all carbon analog. For C₆₈BN, the isomers whose BN is located in the most chemically active bonds of C₇₀ (namely B and A) are among the most stable species, of which B is predicted to be the ground state. The stabilities of C₆₈BN decrease and the dipole moments increase with increasing the distance between the heteroatoms. For C₆₆(BN)₂, the lowest energy species is the isomer in which the B–N–B–N bond is formed; For C₆₄(BN)₃, the most stable species should have three BN units located in the same hexagon to form B–N–B–N–B–N ring. The ionization potentials and the affinity energies of the most stable species of BN-doped C₇₀ are almost the same as those of C₇₀ because of the isoelectronic relationship. The ionization potentials and affinity energies depend on the relative position of the heteroatoms in C₆₈BN, the chemical reactivities of the isomers whose heteroatoms are well separated should differ significantly from their all carbon analog.     

First principles study of the structure, electronic state and stability of SinCm anions

Structure, electronic state and energy of Si_nC⁻ and Si_nC⁻₂ (n=1–7) anions have been investigated using the density functional theory. Structural optimization and frequency analysis are performed at the level B3LYP/6-311G(d). The charged-induced structural changes in these anions have been discussed. The strong C–C bond is also favored over C–Si bonds in the Si_nC⁻_m anions in comparison with corresponding neutral cluster. Among different Si_nC⁻ and Si_nC⁻₂ (n=1–7) anions, Si₃C⁻, Si₅C⁻ and Si₂C⁻₂ are most stable. Their stability has a decreasing tendency with the increase in the size of these clusters.     

Ab initio study on the kinetics and mechanisms of the formation of Agn (n = 2–6) clusters

The CCSD(T)/11e-RECP//MP2/11e-RECP method was used to explore the potential energy surfaces (PESs) of the formation of Ag_n (n = 2–6) clusters. Two kinds of reaction mechanisms were revealed in the formation of Ag_n clusters, the association mechanism for the formation of Ag₂, Ag₅, and Ag₆ clusters and the association–isomerization mechanism for the formation of Ag₃ and Ag₄ clusters. Based on the canonical transition state theory, the calculated rate constants of the formation of Ag_n clusters displayed an odd–even effect: the rate constants of formation of Ag_n clusters with odd number were larger than those with even number. The rate constant of formation of Ag₄ was the lowest, whereas that of Ag₅ was the highest among Ag_n (n = 2–6) clusters. The formation of Ag₄ was the most difficult step in the aggregation process of the silver clusters. The formation of Ag₄ may be related with the critical point in the silver aggregation process.     

The interaction between C28 (Td) and X (X=H and F)

Hydrogen and fluorine addition reactions with C₂₈(T_d) have been investigated by the density function theory method at B3LYP/6-31G level. The interaction potential between C₂₈(T_d) and atom X (X=H and F) shows that there are three possible stable isomers of C₂₈(T_d)X (X=H and F) and the average binding energy calculations suggest that C₂₈(T_d)H₄ is the most stable hydrogen adduct among C₂₈(T_d)H_n (n=1–28). Furthermore, by comparisons of the energy between C₂₈(T_d)H and C₂₈(C_s)H we found that the former are more stable than the later, and the structural and energy analysis further indicate that C₂₈(C_s)H is only with a small distortion of C₂₈(T_d)H symmetry. In addition, the transition states, as well as reaction pathways of X transfer reactions between different key points on C₂₈(T_d) representative patch are given to explore the possible reaction mechanism.     

Sandwich-type transition metal complexes [(CBO)n]2M with carbon boronyl ligands (CBO)n (n=4–6)

A density functional theory investigation on a series of sandwich-type transition metal complexes [(CBO)_n]₂M (n=4–6; M=transition metals) with carbon boronyls (CBO)_n as effective aromatic ligands has been presented in this work at B3LYP level. The ground-states of these complexes possess staggered D_nd symmetries, while the corresponding eclipsed D_nh structures exist as transition states with slightly higher energies (within 5.8 kJ/mol). Carbon boronyl complexes [(CBO)_n]₂M are confirmed to be much more stable than their boron carbonyl isomers [(BCO)_n]₂M, which, on the other hand, take eclipsed ground-states with D_nh symmetries. The carbon boronyl complexes [(BCO)_n]₂M proposed in this work parallelize the well-known sandwich-type hydrocarbon complexes [C_nH_n]₂M in coordination chemistry with boronyl groups –BO isolobal to –H atoms in corresponding ligands.     

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.     

Theoretical study on the aromaticity of the bimetallic clusters X2M2 (X=Si, Ge, M=Al, Ga)

Four neutral bimetallic clusters X₂M₂ (X=Si, Ge, M=Al, Ga) are investigated using density functional theory (DFT) and post-HF methods. The calculated results show that each of four X₂M₂ species has two energetically close stable isomers with rhombic structure (D_2h symmetry) and trapezoidal structure (C_2v symmetry) respectively. For the Ge₂Al₂ species the rhombic (D_2h) isomer is the ground state, whereas for other three species Ge₂Ga₂, Si₂Al₂, and Si₂Ga₂, the trapezoidal (C_2v) isomers are the ground states. The calculated magnetic susceptibility anisotropy (χ_anis) and nucleus-independent chemical shift (NICS) indicate that a strong diatropic ring current exists in the two heterocyclic planar isomers, suggesting they are highly aromatic. A detailed molecular orbital analysis further reveals that both heterocyclic isomers possess multiple aromaticity derived from one delocalized π MOs and two delocalized σ MOs.     

Structure and stability of closo-BnHn−2(CO)2 (n = 5–12)

Closo-B_nH_n−2(CO)₂ (n = 5–12), isolobal analogues of closo-C₂B_n−2H_n, have been investigated at the B3LYP/6-311+G^**density functional level of theory. The most stable isomers of closo-B_nH_n−2(CO)₂ are similar to those of closo-C₂B_n−2H_n in geometric patterns apart from closo-B₆H₄(CO)₂, and closo-B_nH_n−2(CO)₂ is much less strained than closo-C₂B_n−2H_n. Energetic analysis identifies closo-B₆H₄(CO)₂, closo-B₁₂H₁₀(CO)₂ and closo-B₁₀H₈(CO)₂ to be most stable, of which the latter two cages have been prepared experimentally. On the basis of the negative and rather large nucleus independent chemical shifts (NICS), closo-B_nH_n−2(CO)₂ are aromatic. To aid further experimental study, the CO stretching frequencies have been computed.     

A theoretical study of protonated OCnOH ions, n=3–8

Since ion-neutral reactions are a major component of the processes driving interstellar chemistry, most reaction network include protonated species. Besides, these ions are able to initiate chemical processes that would not occur with their neutral parents. In this contribution we report a systematic study of the protonated adducts of the OC_nO series (n=3–8) using the B3LYP level of theory. The structures of all possible O-protonated and C-protonated isomers of [OC_nOH⁺] have been determined together with their rotational constants, vibrational frequencies and intensities. Although it appears that these ions belong to two different series, odd-n and even-n, it is found that protonation occurs at the carbons second to the terminal oxygens for all n. The most stable structure is found to be the singlet ion whatever the singlet or triplet spin state of the parent species. However, due to the lack of efficient spin–orbit coupling, only the odd series [OC_nOH⁺] with n=3,5,7 should be formed on the singlet ground state surface. Analysis of the infrared intensities shows that the spectra are dominated by only one or two very strong bands (CC stretching) that carry most of the overall intensity in the 2200–2350 cm⁻¹ region.     

Complexes of cationic coinage metal clusters Mn (M=Cu, Ag, Au; n=1–4) and H2S: a theoretical study

Geometries and vibrational frequencies of complexes of cationic coinage metal clusters M_n⁺ (M=Cu, Ag, Au; n=1–4) and H₂S are computed using density functional theory. Thermochemical values for M_n⁺H₂S decomposition channels involving loss of an H atom, H₂ molecule, M atom, or M₂ molecule are also computed. Significantly different results are obtained for closed-shell (n odd) and open-shell (n even) complexes.     

First principles study of the structure, electronic state and stability of AlnPm cations

Structural and electronic properties of semiconductor binary microclusters Al_nP_m⁺ cations have been investigated using the B3LYP–DFT method in the ranges of n=1,2 and m=1–7. Full structural optimization, adiabatic ionization potentials calculation and frequency analysis are performed with the basis of 6-311G(d). The charge-induced structural changes in these cations have been discussed. The strong P–P bond is also favored over Al–P bonds in the Al_nP_m⁺ cations in comparison with corresponding neutral cluster. With P_m forming the base, adding Al atom(s) in different positions would find the stable structures of Al_nP_m⁺ cations quickly and correctly. Both AlP₄⁺ and AlP₆⁺ are predicted to be species with high stabilities and possible to be produced experimentally.     

Complexes of small neutral gold clusters and hydrogen sulphide: A theoretical study

Binding energies, geometries, charge transfers and vibrational frequencies of complexes of neutral gold clusters Au_n (n = 1–4) and H₂S are computed using density functional theory. The geometries of Au_n and H₂S are little changed upon complex formation but, for the Au₄SH₂ complex, one of the two low-lying Au₄ isomers is more stabilized by H₂S due to intracomplex hydrogen bonding and may be the lowest-energy Au₄SH₂ structure. For the complexes, computed infrared and Raman spectra are discussed with a focus on distinguishing between the two candidates for the lowest-energy Au₄SH₂ structure.     

Synthesis and characterization of 1,3,4-oxadiazole derivatives containing alkoxy chains with different lengths

The synthesis, optical properties, electrochemical properties, electronic structures and applications in electroluminescent device of three series of 1,3,4-oxadiazole derivatives, 1,4-bis[(4-methylphenyl)-1,3,4-oxadiazolyl]phenylene (OXD₁), 5,5′-di-(4-methyl)-2,2′-p-(2,5-bisalkoxyphenylene)-bis-1,3,4-oxadiazole (OXD_2–n) and 1,4-bis[(4-alkoxyphenyl)-1,3,4-oxadiazolyl]phenylene (OXD_3–n) are reported. The molecular structures of the oxadiazole compounds were confirmed by FT-IR, ¹H NMR spectroscopy and elemental analysis. The optical and electrochemical properties of the compounds were investigated by UV–vis absorption and photoluminescence spectroscopy as well as cyclic voltammetry. The results show that introduction of two alkoxy groups whose electron-donating ability is stronger than that of methyl groups increases the electron density of the conjugated segment of OXD_2–n (with side-on alkoxy substituents) and OXD_3–n (with end-on alkoxy substituents), and thus leads to the absorption maximum bathochromic-shift compared to that of OXD₁. The HOMO and LUMO energy levels of the compounds studied are in the range of −2.78 to −2.89 and −5.75 to −6.20 eV. Calculations on the representative compounds by the Dmol³ package of MS Modeling 3.0 revealed that the increase of energy levels in both OXD_2–n and OXD_3–n was due to the change of the frontier molecular orbital distribution in the central benzene ring. The light-emitting devices have been fabricated using blends of MEH-PPV and these compounds as emissive layers, among which, maximum brightness up to 11810 cd m⁻² (8.5 V) has been observed, which is 40 times brighter than that with MEH-PPV. The result of the devices suggested that oxadiazole derivatives studied function well as electron-transporting materials and can be used in LEDs, and thus to enhance the efficiency of LEDs.     

Global minima of (C60)nCa, (C60)nF and (C60)nI clusters

Likely candidates for the lowest potential energy minima of (C₆₀)_nCa²⁺, (C₆₀)_nF⁻ and (C₆₀)_nI⁻ clusters are located using basin-hopping global optimisation. In each case, the potential energy surface is constructed using the Girifalco form for the C₆₀ intermolecular interaction, an averaged Lennard–Jones C₆₀–ion interaction, and a polarisation potential, which depends on the first few non-vanishing C₆₀ multipole polarisabilities. We find that the ions generally occupy the interstitial sites of a (C₆₀)_n cluster, the coordination shell being tetrahedral for Ca²⁺ and F⁻. The I⁻ ion has an octahedral coordination shell in the global minimum for (C₆₀)₆I⁻, however for 12  n  8 the preferred coordination geometry is trigonal prismatic.     

The interaction of fluorosilanes with hydrogen fluoride clusters: strongly blue-shifted hydrogen bonds

The equilibrium structures, binding energies, and vibrational spectra of the complexes formed between hydrogen fluoride clusters (HF)_n (1≤n≤4) and the fluorosilanes SiHF₃, SiH₂F₂, and SiH₃F are investigated within the second-order Møller–Plesset perturbation theory method applying extended basis sets. It is shown that Si–FH–F halogen–hydrogen bonds are formed in the most stable open dimers, SiHF₃–HF, SiH₂F₂HF, and SiH₃FHF. No Si–HF–H hydrogen bonds occur in these dimers. Nevertheless, blue shifts of Si–H stretching frequencies are calculated. All three trimers, fluorosilane–(HF)₂, all three tetramers, fluorosilane–(HF)₃, and two of the pentamers, fluorosilane–(HF)₄, form cyclic structures with strong Si–FH–F halogen–hydrogen bonds and weak Si–HF–H contacts, the latter displaying, nevertheless, strongly blue-shifted Si–H stretching frequencies. These blue shifts are comparable in size to those of the corresponding fluoromethane–(HF)_n complexes and are with about +50 cm⁻¹ for the case n=3 among the largest ever calculated and definitely the largest for Si–H bonds. In the title complexes, the formation of the Si–FH–F halogen–hydrogen bonds induces a substantial stretching of this Si–F bond, which in turn leads to a significant contraction of the fluorosilane Si–H bond in the Si–HF–H hydrogen bond. This disposition of the fluorosilane monomers is demonstrated with the aid of suitable potential energy surface scans and appears to be a prerequisite for the formation of strongly blue-shifted hydrogen bonds.     

Stereochemical patterns in bromofullerenes C60Br2 to C60Br12

The stabilities of different isomers of C₆₀Br_n have been calculated for n = 2 to 12. A general stereochemical pattern which emerges is the tendency to form strings created by the edge sharing of C₆Br₂ hexagonal faces. Stable structures are formed if these strings form loops, thereby eliminating string ends, which may involve the creation of C₆Br₃ hexagonal faces. A particularly stable structure is formed at C₆₀Br₆ in which the loop forms a C₁₀Br₆ fragment with a pentagonal pyramidal arrangement of six bromine atoms. Two isomers of C₆₀Br₁₂ are also particularly stable. One isomer contains two of these Br₆ pentagonal pyramids on opposite sides of the molecule, and the other isomer contains a single large loop wrapped around the middle of the molecule.