Double icosahedron‐based motif of Nin (n = 20−30)

A genetic algorithm (GA) coupled with a tight‐binding (TB) interatomic potential was used to search for the low‐energy structures of the medium‐sized Ni_n (n = 20?30) clusters. The low‐energy candidate structures from the GA/TB search were further optimized by using the density functional theory calculations with the Perdew, Burke, and Ernzerhof exchange‐correlation energy functional. The obtained lowest‐energy structures of the medium‐sized Ni_n (n = 20?30) clusters are shown to exhibit double icosahedron‐based motif. The properties of the nickel clusters including binding energies, second differences in energy, and especially magnetic properties have also been studied. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Beryllepin,C6H6Be,and “Beryllium‐Inserted Benzenes,” C6H6Ben,n = 2–6: A Density Functional Computational Investigation

The seven‐membered beryllium‐containing heterocycle beryllepin, C₆H₆Be, has been examined computationally at the B3LYP/6‐311++G** density functional level of theory. Beryllepin is best described as a planar singlet heterocyclic conjugated triene with marginal aromatic character containing a C–Be–C moiety forced to be nonlinear (∠C‐Be‐C = 146.25°) by the cyclic constraints of the seven‐membered ring. The molecule can be considered to be derived from a benzene‐like system in which a neutral beryllium atom has been inserted between two adjacent carbon atoms. The 11 other possible “beryllium‐inserted benzenes,” C₆H₆Be_n, n = 2–6, have also been investigated. Only two of these heterocyclic systems, the eight‐membered 1,4‐diberyllocin and the nine‐membered 1,4,7‐triberyllonin, were found to be stable, singlet‐ground‐state systems, albeit with little aromatic character. Of the remaining nine beryllium‐inserted benzenes, with the exception of the 11‐membered ring containing five beryllium atoms and the 12‐membered ring containing six beryllium atoms, which were calculated to exist as a ground state pentet and septet, respectively, all were calculated to be ground state triplet systems.     

Theoretical studies on structures and electronic spectra of linear carbon chains C2nH+ (n = 1−5)

The density functional theory (DFT) and the complete active space self‐consistent‐field (CASSCF) method have been used for full geometry optimization of carbon chains C_2nH⁺ (n = 1–5) in their ground states and selected excited states, respectively. Calculations show that C_2nH⁺ (n = 1–5) have stable linear structures with the ground state of X³Π for C₂H⁺ or X³Σ^? for other species. The excited‐state properties of C_2nH⁺ have been investigated by the multiconfigurational second‐order perturbation theory (CASPT2), and predicted vertical excitation energies show good agreement with the available experimental values. On the basis of our calculations, the unsolved observed bands in previous experiments have been interpreted. CASSCF/CASPT2 calculations also have been used to explore the vertical emission energy of selected low‐lying states in C_2nH⁺ (n = 1–5). Present results indicate that the predicted vertical excitation and emission energies of C_2nH⁺ have similar size dependences, and they gradually decrease as the chain size increases. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Stabilities,electronic properties of exohedral fluorine and trifluoromethyl derivatives for Td C28 fullerene C28F4–n(CF3)n (n = 0,1,2,3,4)

ABSTRACT: Stability and electronic property calculations are performed systematically based on density functional theory at the B3LYP/6‐31G(d) level for T_d C₂₈ fullerene and exohedral fluorine and trifluoromethyl derivatives C₂₈F_4–n(CF₃)_n (n = 0,1,2,3,4). All the exohedral derivatives that are on the potential energy surfaces are kinetically stable with large HOMO‐LUMO gaps. Further investigations show that binding energies of C₂₈F_4–n(CF₃)_n (n = 0,1,2,3,4) molecules are positive, suggesting they are thermodynamically stable. An analysis of the π‐orbital axis vector indicates the high strain in T_d C₂₈ cage could be greatly released by fluorine and trifluoromethyl decorations. Mulliken charge analysis reveals that adding different electron groups to the T_d C₂₈ cage can cause remarkably different charge populations. In addition, from the ionization potential and electron affinity investigations, the C₂₈F_4–n(CF₃)_n (n = 0,1,2,3,4) molecules manifest weak redox properties. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Theoretical studies of structures and stabilities of endohedral fullerenes X0/n+ @C32 (X = H,Li, Na,K, Be,Mg, Ca,B, Al,C, Si,N, P,n = 1–3)

Based on the D₃ C₃₂ fullerene, the equilibrium geometries, electronic structures, and binding energies of the endohedral fullerenes X^0/n+@C₃₂ (X = H, Li, Na, K, Be, Mg, Ca, B, Al, C, Si, N, P, n = 1–3) have been calculated using the DFT/B3LYP/6‐31G(d) method. The results show that the C₃₂ cages are slightly enlarged due to encapsulation, and the sizes of non‐neutral molecules are smaller than the corresponding neutral ones. Cages containing Li, Na, and Ca and most of the cations, except Na⁺ and K⁺, are energetically favorable. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Charge exchange and charge separation processes of [C3Hn]2+ and [C3Dn]2+ (n = 1–6) dications

The charge exchange and charge separation processes of a series of [C₃H_n]²⁺ and [C₃D_n]²⁺ (n = 1–6) dications have been investigated experimentally in a mass spectrometer of reversed geometry. The relative reaction cross-sections for charge exchange with nitrogen exhibited a 20-fold variation which has implications for the interpretation of 2E spectra with respect to dication relative intensities. Charge separation resulting in deprotonation was observed for all [C₃D_n]²⁺ species investigated, while de-deuteronation was observed for [C₃D_n]²⁺ (n = 1–4) only. Intercharge separations calculated from the observed ion kinetic energies released upon charge separation suggest linear structures for [C₃D_n]²⁺ and [C₃D_n]²⁺ (n = 1–2) and cyclic structures for [C₃D_n]²⁺ (n = 3–6) and [C₃D_n]²⁺ (n = 3–4).     

Structure and Stability of C20H3 Radical

Density functional theory B3LYP with 6-31G* basis set has been used to investigate the geometries, rotational constants, dipole moments, energy gaps and vibrational frequencies of nine series of isomers of C20H3 radical. The result shows that the bowl-like structure with C1 symmetry is the most stable structure, in which the three hydrogen atoms locate on the edge carbon atoms, and the two hydrogen atoms are neighbouring and the other one has a two- carbon atom interval to the neighbouring hydrogen. In addition, the relationship between the energy and the position of one hydrogen atom from end to middle on the linear structures of C20H3 radical with two hydrogens atoms located on two ends was obtained, which shows the energy increase monotonously. Furthermore, hydrogenation can relax the strain and make the isomer of C20 more stable.     

Structure and electronic properties of hollow‐caged C60 fullerene‐derived (MN4)nC6(10 − n) (M = Zn,Mg, Fe,n = 1−6) complexes

Unique hollow‐caged (MN₄)_nC_{6(10 ? n)} (M = Zn, Mg, Fe, n = 1?6) complexes designed by introduction of n porphyrinoid fragments in C₆₀ fullerene structure were proposed and the atomic and electronic structures were calculated using LC‐DFT MPWB95 and M06 potentials and 6‐311G(d)/6‐31G(d) basis sets. The complexes were optimized using various symmetric configurations from the highest O_h to the lowest C₁ point groups in different spin states from S = 0 (singlet) to S = 7 (quindectet) for M = Fe to define energetically preferable atomic and electronic structures. Several metastable complexes were determined and the key role of the metal ions in stabilization of the atomic structure of the complexes was revealed. For Fe₆N₂₄C₂₄, the minimum energy was reported for C_2h, D_2h, and D_4h symmetry of pentet state S = 2, so the complex can be regarded as unique molecular magnet. It was found that the metal partial density of states determine the nature of HOMO and LUMO levels making the clusters promising catalysts. © 2014 Wiley Periodicals, Inc.     

Theoretical study in [C2H4–Tl]+ and [C2H2–Tl]+ complexes

We studied the attraction between [C₂H_n] and Tl(I) in the hypothetical [C₂H_n–Tl]⁺ complexes (n = 2,4) using ab initio methodology. We found that the changes around the equilibrium distance C–Tl and in the interaction energies are sensitive to the electron correlation potential. We evaluated these effects using several levels of theory, including Hartree–Fock (HF), second‐order Møller–Plesset (MP2), MP4, coupled cluster singles and doubles CCSD(T), and local density approximation augmented by nonlocal corrections for exchange and correlation due to Becke and Perdew (LDA/BP). The obtained interaction energies differences at the equilibrium distance R_e (C–Tl) range from 33 and 46 kJ/mol at the different levels used. These results indicate that the interaction between olefinic systems and Tl(I) are a real minimum on the potential energy surfaces (PES). We can predict that these new complexes are viable for synthesizing. At long distances, the behavior of the [C₂H_n]–Tl⁺ interaction may be related mainly to charge‐induced dipole and dispersion terms, both involving the individual properties of the olefinic π‐system and thallium ion. However, the charge‐induced dipole term (R^?4) is found as the principal contribution in the stability at long and short distances. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Structure and Bonding in Stannadiphospholes and their Dianions SnC2P2R2m (R=H,tBu m=0, −2): A Comparative Study with C5H5+ and C5H5− Analogues

The potential energy surfaces of both neutral and dianionic SnC₂P₂R₂ (R=H, tBu) ring systems have been explored at the B3PW91/LANL2DZ (Sn) and 6‐311+G* (other atoms) level. In the neutral isomers the global minimum is a nido structure in which a 1,2‐diphosphocyclobutadiene ring (1,2‐DPCB) is capped by the Sn. Interestingly, the structure established by X‐ray diffraction analysis, for R=tBu, is a 1,3‐DPCB ring capped by Sn and it is 2.4 kcal mol^?1 higher in energy than the 1,2‐DPCB ring isomer. This is possibly related to the kinetic stability of the 1,3‐DPCB ring, which might originate from the synthetic precursor ZrCp₂tBu₂C₂P₂. In the case of the dianionic isomers we observe only a 6π‐electron aromatic structure as the global minimum, similarly to the cases of our previously reported results with other types of heterodiphospholes. 1 , 4 , 19 The existence of large numbers of cluster‐type isomers in neutral and 6π‐planar structures in the dianions SnC₂P₂R₂^2? (R=H, tBu) is due to 3D aromaticity in neutral clusters and to 2D π aromaticity of the dianionic rings. Relative energies of positional isomers mainly depend on: 1) the valency and coordination number of the Sn centre, 2) individual bond strengths, and 3) the steric effect of tBu groups. A comparison of neutral stannadiphospholes with other structurally related C₅H₅⁺ analogues indicates that Sn might be a better isolobal analogue to P⁺ than to BH or CH⁺. The variation in global minima in these C₅H₅⁺ analogues is due to characteristic features such as 1) the different valencies of C, B, P and Sn, 2) the electron deficiency of B, 3) weaker pπ–pπ bonding by P and Sn atoms, and 4) the tendency of electropositive elements to donate electrons to nido clusters. Unlike the C₅H₅⁺ systems, all C₅H₅^? analogues have 6π‐planar aromatic structures as global minima. The differences in the relative ordering of the positional isomers and ligating properties are significant and depend on 1) the nature of the π orbitals involved, and 2) effective overlap of orbitals.     

The effects of atom pyramidalization and square distribution on the stability of F4F6‐(BN)n polyhedrons

The structures and stability of F₄F₆‐(BN)_n polyhedrons (n = 20–30) with the alternation of B and N atoms were studied with DFT method. The calculation results reveal that the atoms at square–square fusions with large pyramidalization angles are remarkably extruded out of the surfaces of (BN)_n polyhedrons. The energetically favorable isomers do not contain square–square bonds and the energies of those isomers containing square–square bonds increase with the number of square–square bonds linearly, demonstrating that the energetically favorable structures of F₄F₆‐(BN)_n polyhedrons satisfy the isolated square rule and square adjacency penalty rule. The atom pyramidalization determines the stability of the isomers. The binding energy is fitted to the numbers of vertices formed from different faces and a model is proposed to predict the relative stability of these polyhedral molecules. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

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.     

Singlet–triplet splitting and stability of divalent five‐membered ring C4H4M,C4H6M,and C4H8M (M = C,Si, Ge,Sn, and Pb)

The sum of electronic and thermal free energy differences between singlet and triplet states (Δ G_t‐s) is calculated for C₄H₄M, C₄H₆M, and C₄H₈M (M = C, Si, Ge, Sn, and Pb) at B3LYP/6‐311++G (3df,2p) level. Singlet–triplet splitting (Δ G_t‐s) is compared for three analogs C₄H₄M, C₄H₆M, and C₄H₈M. The change order of Δ G_t‐s is (except for M = C) C₄H₆M > C₄H₈M > C₄H₄M. The results of homodesmotic reaction energies show the most stability for singlet state of C₄H₆M with respect to C₄H₄M and C₄H₈M. In contrast, the triplet state of C₄H₄M (except for M = C) is the most stable with respect to C₄H₆M and C₄H₈M. © 2008 Wiley Periodicals, Inc. Heteroatom Chem 19:245–251, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20428     

Kinetics of phenyl radical reactions with propane,n‐butane,n‐hexane,and n‐octane: Reactivity of C6H5 toward the secondary C?H bond of alkanes

The kinetics of C₆H₅ reactions with n‐C_nH_2n+2 (n = 3, 4, 6, 8) have been studied by the pulsed laser photolysis/mass spectrometric method using C₆H₅COCH₃ as the phenyl precursor at temperatures between 494 and 1051 K. The rate constants were determined by kinetic modeling of the absolute yields of C₆H₆ at each temperature. Another major product C₆H₅CH₃ formed by the recombination of C₆H₅ and CH₃ could also be quantitatively modeled using the known rate constant for the reaction. A weighted least‐squares analysis of the four sets of data gave k (C₃H₈) = (1.96 ± 0.15) × 10¹¹ exp[?(1938 ± 56)/T], and k (n‐C₄H₁₀) = (2.65 ± 0.23) × 10¹¹ exp[?(1950 ± 55)/T] k (n‐C₆H₁₄) = (4.56 ± 0.21) × 10¹¹ exp[?(1735 ± 55)/T], and k (n?C₈H₁₈) = (4.31 ± 0.39) × 10¹¹ exp[?(1415 ± 65)T] cm³ mol^?1 s^?1 for the temperature range studied. For the butane and hexane reactions, we have also applied the CRDS technique to extend our temperature range down to 297 K; the results obtained by the decay of C₆H₅ with CRDS agree fully with those determined by absolute product yield measurements with PLP/MS. Weighted least‐squares analyses of these two sets of data gave rise to k (n?C₄H₁₀) = (2.70 ± 0.15) × 10¹¹ exp[?(1880 ± 127)/T] and k (n?C₆H₁₄) = (4.81 ± 0.30) × 10¹¹ exp[?(1780 ± 133)/T] cm³ mol^?1 s^?1 for the temperature range 297‐‐1046 K. From the absolute rate constants for the two larger molecular reactions (C₆H₅ + n‐C₆H₁₄ and n‐C₈H₁₈), we derived the rate constant for H‐abstraction from a secondary C? H bond, k_s?CH = (4.19 ± 0.24) × 10¹⁰ exp[?(1770 ± 48)/T] cm³ mol^?1 s^?1. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 36: 49–56, 2004     

Exploring Electronic Properties of Si20-n H20-n P n Heterofullerenes (N = 1, 2, 5, and 10) Based on NMR and NBO Analysis: A DFT Study

Abstract

Density functional theory (DFT) calculations are performed to characterize Si_20-nH_20-nP_nheterofullerenes (n = 1, 2, 5, and 10), and to examine the stability of encapsulated X@Si_20-nH_20-nP_nwhere X = Li, Na, and K. To this aim, ²⁹Si, ³¹P, and ¹H chemical shielding (CS) tensors as well as natural charges are calculated for the optimized structures. The local structures around silicon as well as phosphorus nuclei are found to show a good correlation with CSs. However, the similar values of ¹H calculated CSs (26–28 ppm) obtained for all the heterofullerenes mean hydrogen atoms do not detect the local structure around the adjacent silicon and also do not distinguish between isomers of heterofullerenes and the number of P dopants. According to calculated endo-hedral inclusion energies (E_inc), formation of the Li@Si_20-nH_20-nP_ncomplexes, unlike the K@Si_20-nH_20-nP_nones, are exothermic while E_incof the Na@Si_20-nH_20-nP_ncomplexes strongly depends on the position and number of P dopants. Moreover, binding energies for the considered models are found to be in the order of Si_20-nH_20-nP_n> Li@Si_20-nH_20-nP_n> Na@Si_20-nH_20-nP_n> K@Si_20-nH_20-nP_nwhile strongly depending on the pattern of P dopants on the surface of the cage.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the following free supplemental files: Additional figures and tables]     

Theoretical study of two C30H20 isomers with a dodecahedrane cage and two pentaprismane cages sharing two pentagons

Structures, energies, and vibrational frequencies have been calculated for two C₃₀H₂₀ isomers with a dodecahedrane cage and two pentaprismane cages at the B3LYP/6‐31G* level of theory. Thus, two C₃₀H₂₀ isomers have the form of coplanar tri‐cage molecules. The symmetry of one C₃₀H₂₀ isomer is of D_5d and that of another is of C_2V. The heat of formation for two C₃₀H₂₀ isomers have been estimated. Heats of formation of two C₃₀H₂₀ isomers as well as the vibrational analysis indicate that two C₃₀H₂₀ isomers enjoy sufficient stability to allow for its experimental preparation. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Ab initio investigation of water clusters (H2O)n (n = 2–34)

Various properties of typical structures of water clusters in the n = 2–34 size regime with the change of cluster size have been systematically explored. Full optimizations are carried out for the structures presented in this article at the Hartree–Fock (HF) level using the 6‐31G(d) basis set by taking into account the positions of all atoms within the cluster. The influence of the HF level on the results has been reflected by the comparison between the binding energies of (H₂O)_n (n = 2–6, 8, 11, 13, 20) calculated at the HF level and those obtained from high‐level ab initio calculations at the second‐order Møller–Plesset (MP2) perturbation theory and the coupled cluster method including singles and doubles with perturbative triples (CCSD(T)) levels. HF is inaccurate when compared with MP2 and CCSD(T), but it is more practical and allows us to study larger systems. The computed properties characterizing water clusters (H₂O)_n (n = 2–34) include optimal structures, structural parameters, binding energies, hydrogen bonds, charge distributions, dipole moments, and so on. When the cluster size increases, trends of the above various properties have been presented to provide important reference for understanding and describing the nature of the hydrogen bond. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Theoretical Study of the Structures,Properties and Spectroscopies on Fullerene Hydrides C<Subscript>26</Subscript>H<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 2, 4, 6, 8)

The structures, stability patterns of C₂₆H _n (n = 2) formed from the initial D _3h C₂₆ fullerene were investigated by use of second-order-Moller–Plesset perturbation theory. The study of the stability patterns of hydrogenation reaction on C₂₆ cage revealed that type (β) carbons were the active site and the analyses of π-orbital axis vector indicated that the reactivity of C₂₆ was the result of the high strain and the hydrogenation reaction on C₂₆ cage was highly exothermic. The calculated ¹³C NMR spectra of C₂₆H _n (n = 2) predicted that the two sp ³ hybridization carbons in C₂₆H _n (n = 2) obviously moved to high field compare with that in D _3h C₂₆. Hence, the C₂₆H₂ should be obtained and detected experimentally. Similarly, the structures and reaction energies of C₂₆H _n (n = 4, 6, 8) were further studied at HF/6-31G*, B3LPY/6-31G* and MP2/6-31G* level. The results suggested the hydrogenation products of C₂₆, C₂₆H _n (n = 4, 6, 8), were more stable than the C₂₆ cage.     

Towards perfunctionalized dodecahedranes--en route to C20 fullerene

“One‐pot” substitution of the twenty hydrogen atoms in pentagonal dodecahedrane (C₂₀H₂₀) by OH, F, Cl, and Br atoms is explored. Electrophilic insertion of oxygen atoms with DMDO and TFMDO as oxidizing reagents ended, far off the desired C₂₀(OH)₂₀, in complex polyol mixtures (up to C₂₀H₁₀(OH)₁₀ decols, a trace of C₂₀H(OH)₁₉?). Perfluorination was successful in a NaF matrix but (nearly pure) C₂₀F₂₀ could be secured only in very low yield. “Brute‐force” photochlorination (heat, light, pressure, time) provided a mixture of hydrogen‐free, barely soluble C₂₀Cl₁₆ dienes in high yield and C₂₀Cl₂₀ as a trace component. Upon electron‐impact ionization of the C₂₀Cl₁₆ material sequential loss of the chlorine atoms was the major fragmentation pathway furnishing, however, only minor amounts of chlorine‐free C₂₀⁺ ions. “Brute‐force” photobrominations delivered an extremely complex mixture of polybromides with C₂₀HBr₁₃ trienes as the highest masses. The MS spectra exhibited exclusive loss of the Br substituents ending in rather intense singly, doubly, and triply charged C₂₀H_4–0^+(2+)(3+) ions. The insoluble ～C₂₀HBr₁₃ fraction (C₂₀Br₁₄ trienes as highest masses) obtained along a modified bromination protocol, ultimately allowed the neat mass selection of C₂₀^? ions. The C₂₀Cl₁₆ dienes and C₂₀H_0–3Br_14–12 tri‐/tetraenes, in spite of their very high olefinic pyramidalization, proved resistant to oxygen and dimerization (polymerization) but added CH₂N₂ smoothly. Dehalogenation of the respective cycloaddition products through electron‐impact ionization resulted in C_22–24H_4–8⁺⁽²⁺⁾ ions possibly constituting bis‐/tris‐/tetrakis‐methano‐C₂₀ fullerenes or partly hydrogenated C₂₂, C₂₃, and C₂₄ cages.     

Experimental Evidence of Intramolecular CAr–H···O=C Hydrogen Bonds in the Structure of (Diaryl)tetrahydrofuranones Using Spectroscopic Tools

The occurrence of bifurcate H‐bonds C_Ar–H···O=C in the structure of (diaryl)‐tetrahydrofuranones was experimentally demonstrated using different methods and techniques. The consistent increasing spin–spin coupling constants ¹J(C,H) of the ortho‐H‐atoms and low‐field shift of v_C=O in IR spectra of 2,2‐(diaryl)tetrahydrofuran‐3(2H)‐ones relative to their 5,5‐diaryl counterparts, as well as pronounced dependence of the ortho‐C–H H‐atoms chemical shifts on the temperature and solvent polarity along with X‐ray diffraction analysis data unambiguously point to the existence of weak C_Ar–H···O=C H‐bonds in these molecules.