Geometries and electronic structures of W4 and W clusters

Geometries and electronic structures of W₄ and W clusters were studied by use of density functional methods B3LYP, B3P86, B3PW91, BHLYP, BLYP, and MPW1PW91. The calculated results indicate that the three‐dimensional structure of singlet state with either D_2d symmetry (B3LYP, B3P86, B3PW91, BLYP, and MPW1PW91) or C_2v symmetry (BHLYP) is the ground state for the W₄ cluster. For the W cluster, the doublet state is preferred, and the most stable structure is also 3D with either D_2d symmetry (B3LYP, B3PW91, BHLYP, BLYP) or C_2v symmetry (B3P86 and MPW1PW91). The calculated electron affinity at B3P86 gives the best performance compared with experiment. For the dissociation channel, W + W₃ is suggested to be the possible route for the W₄ cluster. For the W cluster, W + W is the most likely route for dissociation, in agreement with experiment. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Geometries and electronic structures of metastable C2N4 and its ions

We carried out the computational studies on the geometric and electronic properties of electronic states of metastable C(2)N(4) (m-C(2)N(4)) and corresponding ions using the CASSCF and DFT(B3LYP)/CCSD(T) techniques. The optimized geometries of electronic states, vibrational frequencies, Mulliken populations, bond orders, and average polarizabilities are computed at the DFT level while the relative energies of the electronic states, ionization energy, electron affinity, binding energy of m-C(2)N(4) are calculated at the CCSD(T) level. The anion photoelectron spectra of m-C(2)N(4)(-) are also predicted. It is interesting to find that the relative energies of the electronic states of m-C(2)N(4) cluster linearly correlate with the amount of charge transfer between N and C atoms and that, however, there is no charge transfer between C and N atoms upon electron ionization or electron attachment.     

Experimental and theoretical studies on carbon-nitrogen clusters C2nN7-

C(2n)N7(-) cluster ions are produced by laser ablating on the K(3)[Fe(CN)6] sample. DFT calculations have been performed for these cluster anions. Various isomeric structures of these clusters are optimized and their energies are compared to find the most stable isomers. The most stable structure for C8N7(-) is similar to that of adenine by theoretical calculation, which is in agreement with the collision-induced dissociation (CID) experimental results. With the increasing even numbers of C atoms from 8 to 16, the N atoms in the double-ring structure are gradually substituted by C atoms from the six-membered ring to the five-membered ring. All these C(2n)N7(-) (n = 3-9) clusters exhibit planar aromatic characters. The energy difference and incremental binding energy analyses show that C(2n)N7(-) (n = 4-8) clusters are more stable than C6N7(-) and C18N7(-), which are consistent with the observed mass spectrum.     

Geometries and electronic properties of the tungsten-doped germanium clusters: WGen (n = 1-17)

Geometries associated with relative stabilities, energy gaps, and polarities of W-doped germanium clusters have been investigated systematically by using density functional theory. The threshold size for the endohedral coordination and the critical size of W-encapsulated Gen structures emerge as, respectively, n = 8 and n = 12, while the fullerene-like W@Ge(n) clusters appears at n = 14. The evaluated relative stabilities in term of the calculated fragmentation energies reveal that the fullerene-like W@Ge(14) and W@Ge(16) structures as well as the hexagonal prism WGe(12) have enhanced stabilities over their neighboring clusters. Furthermore, the calculated polarities of the W@Ge(n) reveal that the bicapped tetragonal antiprism WGe(10) is a polar molecule while the hexagonal prism WGe(12) is a nonpolar molecule. Moreover, the recorded natural populations show that the charges transfer from the germanium framework to the W atom. Additionally, the WGe(12) cluster with large highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap, large fragmentation energy, and large binding energy is supposed to be suitable as a building block of assembly cluster material. It should be pointed out that the remarkable features of W@Ge(n) clusters above are distinctly different from those of transition metal (TM) doped Ge(n) (TM = Cu and Ni) clusters, indicating that the growth pattern of the TMGe(n) depends on the kind of doped TM impurity.     

Geometries and electronic structures of negatively charged carbon clusters

Self-consistent field molecular orbital calculations have been performed on neutral and negatively charged clusters of carbon atoms using an extended basis set designed to obtain correct electron affinity. Correlation effects have been included perturbatively up to second order. The optimized geometries of theC _n ^? (n ≤ 7) anions are all linear chains as observed in experiments. The calculated electron affinities are comparable with experimental data. Studies of the stabilities of doubly charged anions show that clusters uptoC ₇ ^?? are unstable.     

Structures and electronic and magnetic properties of the 3d transition metal-substituted TMC5N8 clusters

Research on Chemical Intermediates - The structures and electronic and spin properties of the 3d TMC5N8 clusters have been calculated using the PBE functional. The results demonstrate that the Zn...     

The electronic and molecular structure of carbon clusters: C8 and C10

Summary The equilibrium geometries of C₈ and C₁₀ have been determined from electronic structure calculations, using a variety of correlated methods and large basis sets of atomic natural orbitals. For C₈, a cyclic form withC _4h symmetry (¹ A _g) and a linear, cumulene-like form (³ _g ^– ) are isoenergetic candidates for the electronic ground state. For C₁₀, the ground-state equilibrium structure is definitely monocyclic. Three different cyclic structures have been considered here, i.e. cumulenicD _10h , distorted-cumulenicD _5h and acetylenicD _5h . These are all essentially isoenergetic, and are about 50 kcal/mol below the linear³ _g ^– state. The choice of basis sets and methods used has a strong impact on the predicted ground-state structures.Dedicated to Prof. Klaus Ruedenberg     

Geometries, electronic states, and spectroscopic properties of nitrogen-doped fullerene fragment C10N2(II) and its ions

The DFT(B3LYP)/6-31G(d)//CCSD(T)/6-31G(d) method is used to investigate the low-lying electronic states of C(10)N(2)(II) and its ions. Mulliken populations, leading configurations, bond orders, and compositions of molecular orbitals are employed to explore the nature of bonding in the electronic states of C(10)N(2)(II) and its ions. Electron affinity, ionization energy, binding energy of C(10)N(2)(II), and anion photoelectron spectra of C(10)N(2)(II)(-) are also estimated at the CCSD(T)/6-31G(d) level. On the other hand, the similarities and differences between C(10)N(2)(I) and C(10)N(2)(II) are compared and discussed.     

Geometries, stabilities, and electronic properties of Pt-group-doped gold clusters, their relationship to cluster size, and comparison with pure gold clusters

A systematic study of bimetallic Au(n)M(2) (n = 1-6, M = Ni, Pd, and Pt) clusters is performed by using density functional theory at the B3LYP level. The geometric structures, relative stabilities, HOMO-LUMO gaps, natural charges and electronic magnetic moments of these clusters are investigated, and compared with pure gold clusters. The results indicate that the properties of Au(n)M(2) clusters for n = 1-3 diverge more from pure gold clusters, while those for n = 4-6 show good agreement with Au(n) clusters. The dissociation energies, the second-order difference of energies, and HOMO-LUMO energy gaps, exhibiting an odd-even alternation, indicate that the Au(4)M(2) clusters are the most stable structures for Au(n)M(2) (n = 1-6, M = Ni, Pd, and Pt) clusters. Moreover, we predict that the average atomic binding energies of these clusters should tend to a limit in the range 1.56-2.00 eV.     

Geometries, stabilities, and electronic properties of small anion Mg-doped gold clusters: a density functional theory study

First-principle density functional theory is used for studying the anion gold clusters doped with magnesium atom. By performing geometry optimizations, the equilibrium geometries, relative stabilities, and electronic and magnetic properties of [Au(n)Mg]? (n = 1-8) clusters have been investigated systematically in comparison with pure gold clusters. The results show that doping with a single Mg atom dramatically affects the geometries of the ground-state Au(n+1)? clusters for n = 2-7. Here, the relative stabilities are investigated in terms of the calculated fragmentation energies, second-order difference of energies, and highest occupied?lowest unoccupied molecular orbital energy gaps, manifesting that the ground-state [Au(n)Mg]? and Au(n+1)? clusters with odd-number gold atoms have a higher relative stability. In particular, it should be noted that the [Au?Mg]? cluster has the most enhanced chemical stability. The natural population analysis reveals that the charges in [Au(n)Mg]? (n = 2-8) clusters transfer from the Mg atom to the Au frames. In addition, the total magnetic moments of [Au(n)Mg]? clusters exhibit an odd-even oscillation as a function of cluster size, and the magnetic effects mainly come from the Au atoms.     

Geometries and electronic structures of nitrogen-doped fullerene fragment C10N2(I) and its ions

The geometries and relative energies of the low-lying electronic states of C(10)N(2)(I), cation, and anion are investigated by the DFT/CCSD(T) method. Vibrational frequency calculation is performed to analyze the stability of optimized geometries of these states. The binding energy, ionization energy, electron affinity of C(10)N(2)(I) and the anion photoelectron spectra are estimated at the CCSD(T)/6-31G(d) level. The ground states of neutral C(10)N(2)(I), cation, and anion are the (1)A(1), (4)B(2), and (2)A(2) states, respectively. The structure of C(10)N(2)(I) can be described as resulting from the fusion of 2 five-numbered rings and 1 six-numbered ring. Results demonstrate that the 2 five-numbered rings are more active than the six-numbered ring in C(10)N(2)(I) during electron excitation and the C(1) atom site within each N(11)-C(1)-C(5)-C(10) unit exhibits more inert than other atom sites during electron ionization and electron attachment.     

Structure and electronic properties of TI8C12 cluster

Structure and electronic properties of recently discovered Ti₈C₁₂ molecule are studied using the discrete variational method within the framework of local density approximation. The geometry of this novel cluster is optimized to be a distorted dodecahedron by varing the bond lengths of Ti-C and C-C while maintaining theT _h symmetry, and the electronic states and the chemical bonding are discussed.     

Geometries, stabilities, and electronic properties of different-sized ZrSi(n) (n=1-16) clusters: a density-functional investigation

The ZrSi(n) (n=1-16) clusters with different spin configurations have been systematically investigated by using the density-functional approach. The total energies, equilibrium geometries, growth-pattern mechanisms, natural population analysis, etc., are discussed. The equilibrium structures of different-sized ZrSi(n) clusters can be determined by two evolution patterns. Theoretical results indicate that the most stable ZrSi(n) (n=1-7) geometries, except ZrSi3, keep the analogous frameworks as the lowest-energy or the second lowest-energy Si(n+1) clusters. However, for large ZrSi(n) (n=8-16) clusters, Zr atom obviously disturbs the framework of silicon clusters, and the localized position of the transition-metal (TM) Zr atom gradually varies from the surface insertion site to the concave site of the open silicon cage and to the encapsulated site of the sealed silicon cage. It should be mentioned that the lowest-energy sandwich-like ZrSi12 geometry is not a sealed structure and appears irregular as compared with other TM@Si12 (TM = Re,Ni). The growth patterns of ZrSi(n) (n=1-16) clusters are concerned showing the Zr-encapsulated structures as the favorable geometries. In addition, the calculated fragmentation energies of the ZrSi(n) (n=1-16) clusters manifest that the magic numbers of stabilities are 6, 8, 10, 14, and 16, and that the fullerene-like ZrSi16 is the most stable structure, which is in good agreement with the calculated atomic binding energies of ZrSi(n) (n=8-16) and with available experimental and theoretical results. Natural population analysis shows that the natural charge population of Zr atom in the most stable ZrSi(n) (n=1-16) structures exactly varies from positive to negative at the critical-sized ZrSi8 cluster; furthermore, the charge distribution around the Zr atom appears clearly covalent in character for the small- or middle-sized clusters and metallic in character for the large-sized clusters. Finally, the properties of frontier orbitals and polarizabilities of ZrSi(n) are also discussed.     

The structural and electronic properties of In(n)N(n = 1-13) clusters

The structural and electronic properties of In(n)N(n=1-13) clusters have been investigated by density-functional theory with the generalized gradient approximation. The results indicate that the equilibrium structures of In(n)N are linear for n=1,2, planar for n=3-5, and three dimensional for n=6-13. Maximum peaks were observed for In(n)N clusters at n=3,7,9 on the size dependence for second-order energy difference. These imply that these clusters possess relatively higher stability, which is consistent with the case of binding energy per atom. Moreover, the results show that the bonding in small In(n)N clusters has a little ionic character by Mulliken population analysis. The energy gap between the highest occupied and lowest unoccupied molecular orbitals, the vertical ionization potential and electron vertical affinity (VIP and VEA) form an even-odd alternating pattern with increasing cluster size. In general, the VIP tends to lower as the cluster size increases, while the VEA tends to increase as the cluster size increases.     

Geometric and electronic structures of multiple-decker one-end open sandwich clusters: Eu(n)(C8H8)n- (n = 1-4)

We have measured the photoelectron spectra of the multiple-decker 1:1 sandwich clusters of Eu(n)(COT)n- (n = 1-4; COT = 1,3,5,7-cyclooctatetraene), synthesized in the gas phase, and studied theoretically the bonding scheme, charge distribution, valence orbital energies, and photodetachment energies. We calculated the ground electronic state X- and the first excited electronic state A-, both of which have strong ionic bonding and a characteristic charge distribution. Moreover, we found that the valence orbital energies of Eu (6s) and COT (L delta) depend strongly on cluster size and their positions in the clusters. With the calculated vertical detachment energies for these valence orbitals, we assigned the peaks in the experimental photoelectron spectra and analyzed the origin of their interesting behavior by employing simple point charge models. From these analyses, it became clear that the characteristic behavior of the spectra is due to the strong ionic bonding and the charge distribution. In addition, using the point charge models, we estimated the vertical detachment energies of the one-dimensional polymer [Eu(COT)]infinity-.     

Thermal electronic properties of alkali clusters

We apply the finite-temperature Kohn-Sham method to alkali metal clusters, using the spherical jellium model and treating the valence electrons as a canonical system in the heat bath of the ions. We study the shell effects in the total free energyF(N) and the entropyS(N) for neutral clusters containingN atoms. Their strongest temperature dependence is due to the finite ground-state valueS ₀>0 of the electronic entropy for non-magic clusters. It leads to a decreasing amplitude and an increasing smear-out of the saw-tooth structure in the first difference Δ₁ F(N)=F(N?1)?F(N) with increasing temperatureT and cluster sizeN.     

Structures and magnetic and electronic properties of the O2-adsorbed Fe2N clusters

Structural Chemistry - The surface of iron nitrides prefers to be oxidized in the air, which reduces the cycling stability of the supercapacitors. The configurations and electronic and magnetic...     

Evolution of the electronic properties of Snn- clusters (n=4-45) and the semiconductor-to-metal transition

The electronic structure of Sn(n) (-) clusters (n=4-45) was examined using photoelectron spectroscopy at photon energies of 6.424 eV (193 nm) and 4.661 eV (266 nm) to probe the semiconductor-to-metal transition. Well resolved photoelectron spectra were obtained for small Sn(n) (-) clusters (n< or =25), whereas more congested spectra were observed with increasing cluster size. A distinct energy gap was observed in the photoelectron spectra of Sn(n) (-) clusters with n< or =41, suggesting the semiconductor nature of small neutral tin clusters. For Sn(n) (-) clusters with n> or =42, the photoelectron spectra became continuous and no well-defined energy gap was observed, indicating the onset of metallic behavior for the large Sn(n) clusters. The photoelectron spectra thus revealed a distinct semiconductor-to-metal transition for Sn(n) clusters at n=42. The spectra of small Sn(n) (-) clusters (n< or =13) were also compared with those of the corresponding Si(n) (-) and Ge(n) (-) clusters, and similarities were found between the spectra of Sn(n) (-) and those of Ge(n) (-) in this size range, except for Sn(12) (-), which led to the discovery of stannaspherene (the icosahedral Sn(12) (2-)) previously [L. F. Cui et al., J. Am. Chem. Soc. 128, 8391 (2006)].     

Structural and electronic properties of compound metal clusters

The equilibrium geometries, relative stabilities, and vertical ionization potentials of compound clusters involving Li _n , Na, Mg, and Al atoms have been calculated using ab initio self-consistent field linear combination of atomic orbitals — molecular orbital (SCF-LCAO-MO) method. The exchange energies are calculated exactly using the unrestricted Hartree-Fock (UHF) method whereas the correlation correction is included within the framework of configuration interaction involving pair excitations of valence electrons. While the later correction has no significant effect on the equilibrium geometries of clusters, it is essential for the understanding of relative stabilities. Clusters with even numbers of electrons are found to be more stable than those with odd numbers of electrons regardless of their charge state and atomic composition. The equilibrium geometries of homo-nuclear clusters can be significantly altered by replacing one of its constituent atoms with a hetero-nuclear atom. The role of electronic structure on the geometries and stabilities of compound clusters is discussed.     

Structural and electronic properties of neutral and ionic Ga(n)On clusters with n = 4-7

We report the results of a theoretical study of neutral, anionic, and cationic Ga(n)On clusters (n = 4-7), focusing on their ground-state configurations, stability, and electronic properties. The structural motif of these small gallium oxide clusters appears to be a rhombus or a hexagonal ring with alternate gallium and oxygen atoms. With the increase in the cluster size from Ga4O4 to Ga7O7, the ground-state configurations show a transition from planar to quasi-planar to three-dimensional structure that maximizes the number of ionic metal-oxygen bonds in the cluster. The ionization-induced distortions in the ground state of the respective neutral clusters are small. However, the nature of the LUMO orbital of the neutral isomers is found to be a key factor in determining the ordering of the low-lying isomers of the corresponding anionic clusters. A sequential addition of a GaO unit to the GaO monomer initially increases the binding energy, though values of the ionization potential and the electron affinity do not show any systematic variation in these clusters.