Geometrical and Electronic Properties of the Clusters of C<Subscript>20</Subscript> Cage Doped with Alkali Metal Atoms

Using first-principles density-functional theory based on the generalized gradient approximation, we have investigated the geometrical and electronic properties of the pure C₂₀ cage with D _3d symmetry and M@C₂₀(M = Li, Na, K, Rb, Cs) clusters with I _h symmetry. It is found that the interstitial M@C₂₀ clusters are energetically stable and have strong total magnetic moments. The stability is analyzed through charge distributions on the atoms and the magnetism is explained through the degeneracy and fractional occupation of the molecular orbitals.     

A study of the electronic structure of polyvinylsiloxane (CH<Superscript>2</Superscript>CHSiO<Subscript>1.5</Subscript>)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> by X-ray photoelectron spectroscopy and quantum chemical modeling in the DFT approximation

The electronic structure of polyvinylsiloxane polymeric chains (Si₂O₃(CHCH₂)₂)_n is studied by X-ray photoelectron spectroscopy and quantum chemistry in the DFT approximation. The binding energy of C and O ls electrons occupying inequivalent positions in the polymer coincides within the experimental accuracy. The binding energies for C and O (284.9 eV and 532.4 eV) and for Si2p-electrons (102.7 eV) well agree with the values for related compounds. The experimental data for the binding energy are reproduced in HF and DFT calculations only with the extended 6–311**(d) basis set. The highest occupied levels of the polymer are fy orbitals of vinyl groups     

Theoretical modeling of dissociative addition of an H<Subscript>2</Subscript> molecule to doped aluminum clusters FeAl<Subscript>12</Subscript> and CoAl<Subscript>12</Subscript>

The potential energy surfaces (PES) of the reactions FeAl₁₂ + Н₂ → FeН₂Al₁₂ (1) and CoAl₁₂ + Н₂ → CoН₂Al₁₂ (2) of dissociative addition of an H₂ molecule to Fe- and Co-doped aluminum clusters have been calculated by the density functional theory method. Local minima on the PES in the vicinity of low-lying isomers, intermediates, and transition states have been found, and their structural and spectroscopic characteristics and energies have been calculated. The energies of the successive stages of the catalytic cycle have been evaluated, and the channels corresponding to the minimum energy path of the reactions have been studied. Differences between the structural characteristics and energies of key structures in reactions (1) and (2) have been considered. The results are compared with previous calculations of the PES of hydrogenation reactions performed for related clusters doped with nickel and titanium atoms.     

Structures and electronic properties of C<Subscript>12</Subscript>Si<Subscript>8</Subscript>X<Subscript>8</Subscript> (X = H,F, and Cl)

The structural stabilities and electronic properties of C₁₂Si₈X₈ where X = H, F, and Cl are probed on the basis of density functional theory at the B3LYP/6-311++G**//B3LYP/6-31+G* level. Vibrational frequency calculations show that all the systems are true minima. The infrared spectra of the most stable C₁₂Si₈X₈ molecules are simulated to assist further experimental characterization. The functionalized structures and energy gaps between the highest occupied molecular orbital, HOMO, and the lowest unoccupied molecular orbital, LUMO, have been systematically investigated. It seems that C₁₂Si₈H₈ has more stability against electronic excitations via increasing the HOMO–LUMO gap comparing with C₁₂Si₈Cl₈ and C₁₂Si₈F₈. High charge transfer on the surfaces of our stable compounds, provokes further investigations on their possible application for hydrogen storage. The addition reaction energies of C₁₂Si₈X₈ are high exothermic, and C₁₂Si₈F₈ is more thermodynamically accessible.     

Compositions and structures of nanoparticles of trigonal symmetry <Emphasis Type="Italic">D</Emphasis><Subscript>3<Emphasis Type="Italic">d</Emphasis></Subscript>: Nanotubes

A method has been developed for the determination of the structure and number of atoms in the shells of nanoparticles as a function of the arrangement of atoms at the symmetry elements of a symmetry group. The formulas for calculation of the number of particles of symmetry D _3d have been reported. It has been shown that the number of atoms in trigonal shells is determined by three structurally invariant numbers and the quantum number of the group order n. All possible nanostructures of symmetry D _3d have been classified: C_{θ + 6z} , z = 0, 1, 2, ..., where the basic shells are C_θ = C₆, C₈, and C₁₄. A sum rule has been obtained for the coordination numbers of the shell sites located on symmetry axes. Trigonal nanoparticles are parent ones for obtaining (3,0), (6,0), and (9,0) nanotubes of trigonal type. The general formulas of these nanotubes with icosahedral, dodecahedral, and cubic caps are N_{8 + 12p} , N_{20 + 24p} , and N_{60 + 36p} (p = 1, 2, ...), respectively. The graphical constructions of all classes of trigonal nanoparticles and nanotubes are reported.     

Trends in the formation of aggregates and crystals from M@Si<Subscript>16</Subscript> clusters: a study from first principle calculations

We have shown recently that the ground state and low-lying energy isomers of the endohedral M@Si₁₆ clusters (M = Sc⁻, Ti, V⁺) have a nearly spherical cage-like symmetry with a closed shell electronic structure which conforms them as exceptional stable entities. This is manifested, among other properties, by a large Homo–Lumo gap about 2 eV which suggest the possibility of using these clusters as basic units (superatoms) to construct optoelectronic materials. As a first step in that direction, we have studied in this work, by means of first principles calculations, the trends in the formation of [Ti@Si₁₆] _n , [Sc@Si₁₆K] _n , and [V@Si₁₆F] _n aggregates as their size increases, going from linear to planar to three dimensional arrangements. The most favorable configurations for n ≥ 2 are those formed from the fullerene-like D_4d isomer of M@Si₁₆, instead of the ground state Frank–Kasper T _d structure of the isolated M@Si₁₆ unit, joined by Si–Si bonds between the Si atoms of the square faces. In all cases the Homo–Lumo gap for the most favorable structure decrease with the size n. Trends for the binding energy, dipole moment, and other electronic properties are also discussed. Several crystal structures constructed from these superatom, supermolecules, and aggregates have been tested and preliminary results are summarily commented.     

Theoretical study of isomerism of carbonand silicon-substituted aluminum clusters M<Subscript>6</Subscript>Al<Subscript>38</Subscript> and M<Subscript>12</Subscript>Al<Subscript>32</Subscript>

More than twenty M₆Al₃₈ isomers and several M₁₂Al₃₂ isomers of carbon- and silicon-substituted aluminum clusters with six and twelve dopant atoms of general formula M_nA_l44–n(M = C and Si, n = 6 and 12) have been studied by the density functional theory method. Calculations predict that, in the lowest-lying M₆Al₃₈, isomer, all substitutions of C atoms for Al are localized in one outer surface layer of the aluminum cage. In the course of optimization, the C atoms with a negative charge of about 1e are incorporated into positions of the intermediate layer to transform it into a 12-atom face composed of three adjacent vertex-sharing six-membered rings with short C–Al bonds. In the favorable isomer of M₆Al₃₈, the dopants are scattered as individual Si atoms located in both outer layers or in the subsurface space between the outer layers and the inner core of the cluster. Optimization of low-lying isomers with twelve starting substitutions of C and Si for Al in both outer layers has localized two preferable C₁₂Al₃₂ isomers. One of them contains three covalently bonded diatomic C₂ anions, which are combined through bridging aluminum atoms in the three-dimensional [C₆Al₇] cluster inside the severely distorted outer cage. In the second, most favorable, isomer, the dopants are distributed as isolated C anions; together with the bridging Al atoms, they form the [M₁₂Al₃₂] inner cage with an unusual dumbbell-like structure. For M₁₂Al₃₂, the aluminum cage undergoes moderate distortions. The silicon atoms remain in the outer layers and form five-membered ring subclusters [Si₅] and [Si₂Al₃] bound to the neighboring intermediate layers through elongated and weakened Si–Al bonds. Evaluation of the energies of the model exchange reactions Al₄₄ + M₆ → M₆Al₃₈ + Al₆ and Al₄₄ + 2M₆ → M₁₂Al₃₂ + 2A_l6 shows that for M= C both reaction are exothermic, whereas for M = Si the former reaction is nearly isothermal and the second reaction is endothermic and requires significant energy inputs. The differences between the equilibrium structures and the relative positions on the energy scale of the isomers of the C₆Al₃₈–Si₆Al₃₈ and C₁₂Al₃₈–Si₁₂Al₃₈ clusters are examined.     

Electronic structure of tungsten aluminum carbides W<Subscript>2</Subscript>AlC and WAlC<Subscript>2</Subscript>

The full-potential FLAPW-GGA method was used for the first time to calculate the electronic structure of hexagonal tungsten aluminum carbides W₂AlC and WAlC₂ and their equilibrium structural parameters, density, cohesion energies, formation energies, low-temperature heat capacity coefficients, and Pauli paramagnetic susceptibility. These characteristics are discussed in comparison with analogous parameters for the initial binary carbides WC and Al₄C₃.     

Molecular structures and thermochemistry of the derivatives of C<Subscript>24</Subscript> fullerene by attaching a variety of chemical groups

A series of exohedrally functionalized derivatives of the D ₆-symmetrical C₂₄ fullerene, with attached -CH₂OH, -CONH₂, -COOH, and -COH chemical groups, have been investigated by using density-functional theory approach at the UB3LYP/6-31G(d) level. According to the calculated results, the C₂₄(COOH) is the most stable structure, with −73.58 kcal mol⁻¹ value for the functionalization reaction energy and 3.16 eV for the dissociation energy, while C₂₄(CONH₂) displays the largest dipole moment (3.09 D). It was also found that the HOMO-LUMO energy gaps, the vertical ionization potentials (VIP), and vertical electron affinities (VEA) of these functionalized derivatives are similar to those of the more stable C₂₄ fullerene. Moreover, their corresponding HOMO and LUMO orbitals are mainly associated with the surface of the cage. Also, the vibrational frequencies of these derivatives are discussed. It was concluded that it would be possible to produce novel species for bio-medical applications by attaching selected chemical groups.     

<Emphasis Type="Italic">Ab initio</Emphasis> structural study of M(mda)<Subscript>2</Subscript> complexes (M = Be,Mg, Ca; mda = C<Subscript>3</Subscript>O<Subscript>2</Subscript>H<Subscript>3</Subscript>)

The structure of M(mda)₂ (M = Be, Mg, Ca; mda = C₃O₂H₃) bis-complexes was investigated by the ab initio Hartree-Fock method and by including electron correlation in terms of second order Möller-Plesset perturbation theory; for calculations we used triple-zeta valence basis sets complemented with polarization functions. Two most probable geometrical nuclear configurations (D _2h and D _2d ) are considered for each molecule. The structure with two mutually orthogonal chelate ligands (D _2d symmetry) corresponds to the potential energy surface (PES) minimum. The planar D _2h configuration corresponds to the first order saddle point on PES; consequently, its relative energy determines the height of the barrier to the D _2d D _2h D _2d intramolecular rearrangement. Correlation equations that relate the calculated values of equilibrium internuclear distances, force constants, and rearrangement barrier heights to the value of the ionic radius of the metal atom have been obtained. These correlations were employed to evaluate the molecular constants for Sr(mda)₂ and Ba(mda)₂. The theoretical data are compared with the available experimental literature data.Original Russian Text Copyright © 2004 by V. V. Sliznev, S. B. Lapshina, and G. V. GirichevTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 4, pp. 611–623, July–August, 2004This revised version was published online in April 2005 with a corrected cover date.     

Quantum-chemical study of ytterbium fluorides and of complex F<Subscript>2</Subscript>YbF<Subscript>2</Subscript>CeF<Subscript>2</Subscript>

The structural parameters of the (²Σ⁺//C_∞v)-YbF, (¹A₁//C_2v)-YbF2, (²A₂^′//D_3h)-YbF₃, (¹Ag//D_2h)-YbF₂Yb, (¹Ag//C_2h)-FYbF₂YbF, (¹A₁//C_2v)-FYbF₂YbF, (¹A₁//C_2v)-YbF₂YbF₂, (³B_3u//D_2h)-F₂YbF₂YbF₂, (²A′//C_s)-FYbF₂YbF₂, and (³B₂//С_2v)-F₂YbF₂CeF₂ molecules have been determined. Disproportionation of ytterbium monofluoride (2YbF → YbF₂ + Yb + 0.46 eV) is less exothermic than dimerization (2YbF → YbF₂Yb + 2.10 eV). The bond energy of the ytterbium difluoride molecules in the trans dimer (2.93 eV) exceeds those in the cis dimer (2.86 eV) and the coaxial dimer (1.66 eV). Ytterbium trifluoride dimerizes exothermically (2.95 eV) without spin pairing. The dipole and quadrupole moments of the molecules as well as the charges and spin populations of the atoms and the valence electron configurations of the lanthanides have been calculated.     

Theoretical investigation of the equilibrium structure of the FSO<Subscript>3</Subscript> radical

Six different theoretical approaches (MP2, DFT-B3LYP/MPW3LYP, QCISD, UHF/ROHF-CCSD, UHF/ROHF-CCSD[T], and EOMIP-CCSD) were employed for a detailed theoretical investigation of a minimum on the potential surface of the fluorosulfate radical FSO₃ ground state. Optimized geometries, spin distributions, vibrational frequencies, and centrifugal distortion constants were calculated within C _3v and C ₁ initial symmetry constraints.     

Molecular structure of NiO<Subscript>2</Subscript>N<Subscript>2</Subscript>C<Subscript>16</Subscript>H<Subscript>14</Subscript> from gas-phase electron diffraction and quantum chemical data

Gas-phase electron diffractometry was used to study the molecular structure of N,N′-ethylenebis(salicylaldiminato)nickel(II), NiO₂N₂C₁₆H₁₄, [hereinafter Ni(salen)] at 583(5) K. The molecule has C ₂ symmetry with a practically planar structure of the NiN₂O₂ coordination unit and with internuclear distances r _α (Ni-O) = 1.882(21) Å and r _α (Ni-N) = 1.889(22) Å. The results of B3LYP/CEP-31G molecular structure calculations are in good agreement with experimental data, whereas the RHF/CEP-31G method significantly overestimates the Ni-N internuclear distance and gives worse results for other structural parameters. According to 3LYP/CEP-31G calculations, the ¹ A low-spin state is 28 kJ/mole lower in energy than the ³ B high-spin state.     

Compositions and structures of nanoparticles of pentagonal axial symmetry <Emphasis Type="Italic">D</Emphasis><Subscript>5<Emphasis Type="Italic">d</Emphasis></Subscript>: Nanotubes

The method of determination of the structure and the number of atoms in the shells of nanoparticles as a function of the arrangement of atoms at the symmetry elements of a symmetry group has been developed. The formulas for the calculation of the number of particles with symmetry group D _5d are reported. The number of particles in these shells is determined by three structurally invariant numbers and the “quantum number” of the group order n. The classification of all possible nanostructures with symmetry group D _5d is given: C _θ+10z , z = 0, 1, 2, …, where the basic shells are C _θ = C ₂, C ₁₀, C ₁₂. The sum rule has been obtained for the coordination numbers of shell sites located at symmetry axes. Pentagonal axial nanoparticles are shown to be the initial shells for obtaining (5,5) and (10,10) armchair nanotubes or (5,0) and (10,0) zigzag nanotubes. The general formula of these nanotubes closed with icosahedral and dodecahedral caps is N _20+10p , N _60+10p (p = 1, 2, …). The graphical constructions of all classes of nanoparticles and nanotubes of the pentagonal axial type are reported.     

Resonant emission of UO<Subscript>2</Subscript>, U<Subscript>3</Subscript>O<Subscript>8</Subscript>, and UO<Subscript>2+<Emphasis Type="Italic">x</Emphasis></Subscript> valence electrons under SR excitation near the O<Subscript>4,5</Subscript>(U) absorption edge

The structure of the resonant electron emission (REE) spectra of UO₂ (REE appears under the excitation with synchrotron radiation near the O_4,5(U) absorption edge at ∼100 eV and ∼110 eV) is studied with regard to the X-ray O_4,5(U) absorption spectrum of UO₂ and a quantitative scheme of molecular orbitals based on the X-ray electron spectroscopy data and the results of a relativistic calculation of the electronic structure of UO₂. The structure of the REE spectra of U₃O₈ and UO_2+x is studied for comparison, and the effect of the uranium chemical environment in oxides on it is found. The appearance of such a structure reflects the processes of excitation and decay involving the U5d and electrons of the outer valence MOs (OVMOs, from 0 to ∼13 eV) and inner valence MOs (IVMOs, from ∼13 eV to ∼35 eV) of the studied oxides. It is noted that REE spectra show the partial density of states of U6p and U5f electrons. Based on the structure of REE spectra, it is revealed that U5f electrons directly participate (without losing the f nature) in the chemical bonding of uranium oxides and are delocalized within CMOs (in the middle of the band), which results in the enhancement of the intensity of the REE spectra of CMO electrons during resonances. The U6d electrons are found to be localized near the bottom of the outer valence band and are observed in the REE spectra of the studied oxides as a characteristic maximum at 10.8 eV. It is confirmed that U6p electrons are effectively involved in the formation of IVMOs, which leads to the appearance of the structure in the region of IVMO electron energies during resonances. This structure depends on the chemical environment of uranium in the considered oxides.     

A Quantum Chemical Study of C<Subscript>60</Subscript>Cl<Subscript>30</Subscript>, C<Subscript>60</Subscript>(OH)<Subscript>30</Subscript> Molecules and Fe@C<Subscript>60</Subscript>(OH)<Subscript>30</Subscript> Endocomplex

(U)PBE0/cc-pVDZ method is used to study the structure of C₆₀Cl₃₀, C₆₀(OH)₃₀ molecules and Fe@C₆₀(OH)₃₀ endocomplex. The triplet state of the endocomplex is shown to be the lowest in energy among its four states corresponding to different spin multiplicities and positions of Fe nucleus within the fullerene cavity. This state is characterized by bonding between the iron atom and one of two benzenoid cycles of the carbon cage, six internuclear Fe–C distances (208 pm), and 1s²2s²2p⁶3s²3p⁶3d^7.24s^0.14p^0.3 electron configuration of iron with spin population of 2.36.     

Quantum-chemical DFT calculations of the molecular structure of N<Subscript>2</Subscript>O<Subscript>5</Subscript> in the gas and solid phases

By functional density quantum-chemical method (DFT/B3LYP using the 6-311++G(3df)) it has been shown that the molecular structures of N₂O₅ with C_s and C₂ symmetries are energetically equivalent. It follows from calculations of the vibrational frequencies that both structures are characterized by potential energy minima and correspond to stationary states of the N₂O₅ molecule. It is proposed, on the basis of a comparison of the calculated and experimental vibrational spectra of N₂O₅, that dinitrogen pentaoxide exists in the gas phase as an equimolecular mixture of N₂O₅ molecules with Cs and C₂ symmetry, while in the solid phase it is characterized by the C₂ molecular structure. __________ Translated from Teoreticheskaya I éksperimental’naya Khimiya, Vol. 43, No. 1, pp. 58–63, January–February, 2007.     

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.     

Relative Raman Intensities in C<Subscript>6</Subscript>H<Subscript>6</Subscript>, C<Subscript>6</Subscript>D<Subscript>6</Subscript>, and C<Subscript>6</Subscript>F<Subscript>6</Subscript>: A Comparison of Different Computational Methods

The accuracy of various computational methods (Hartree–Fock, MP2, CCSD, CAS-SCF, and several types of DFT) for predicting relative intensities in Raman spectra for C₆H₆, C₆D₆, and C₆F₆ was compared. The predicted relative intensities for ν₁ and ν₂ were compared with relative intensities measured by an FT-Raman spectrometer. While none of these methods excelled at this prediction, Hartree–Fock with a large basis set was most successful for C₆H₆ and C₆D₆, while PW91PW91 was the most successful for C₆F₆.     

Endohedral Complex of Fullerene C<Subscript>60</Subscript> with Tetrahedral N<Subscript>4</Subscript>, N<Subscript>4</Subscript>@C<Subscript>60</Subscript>

B3LYP/6-31G(d) hybrid HF/DFT and BLYP/6-31G(d, p) DFT calculations were carried out to determine the structural and electronic properties of the endohedral complex of C₆₀ with Tetrahedral N₄ (T_d N₄), N₄@C₆₀. It was demonstrated that N₄ was seated in the center of the fullerene cage and the tetrahedral structure of N₄ is remained in the cage. The formation of this complex is endothermic with inclusion energy of 37.92 kcal/mol. N₄ endohedral doping perturbs the molecular orbitals of C₆₀ not so much, the calculated HOMO–LUMO gaps, the electron affinity (EA) and the ionizational potential (IP) of N₄@C₆₀ are similar to that of C₆₀.