Structural evolution and stability of hydrogenated Li(n) (n = 1-30) clusters: a density functional study

The structure and electronic and optical properties of hydrogenated lithium clusters Li(n)H(m) (n = 1-30, m ≤ n) have been investigated by density functional theory (DFT). The structural optimizations are performed with the Becke 3 Lee-Yang-Parr (B3LYP) exchange-correlation functional with 6-311G++(d, p) basis set. The reliability of the method employed has been established by excellent agreement with computational and experimental data, wherever available. The turn over from two- to three-dimensional geometry in Li(n)H(m) clusters is found to occur at size n = 4 and m = 3. Interestingly, a rock-salt-like face-centered cubic structure is seen in Li(13)H(14). The sequential addition of hydrogen to small-sized Li clusters predicted regions of regular lattice in saturated hydrogenated clusters. This led us to focus on large-sized saturated clusters rather than to increase the number of hydrogen atoms monotonically. The lattice constants of Li(9)H(9), Li(18)H(18), Li(20)H(20), and Li(30)H(30) calculated at their optimized geometry are found to gradually approach the corresponding bulk values of 4.083. The sequential addition of hydrogen stabilizes the cluster, irrespective of the cluster size. A significant increase in stability is seen in the case of completely hydrogenated clusters, i.e., when the number of hydrogen atoms equals Li atoms. The enhanced stability has been interpreted in terms of various electronic and optical properties like adiabatic and vertical ionization potential, HOMO-LUMO gap, and polarizability.     

A density functional study on nitrogen-doped carbon clusters CnN3- (n=1-8)

Using molecular graphics software, we designed numerous models of CnN3- (n=1-8). Geometry optimization and calculation on vibration frequency were carried out by the B3LYP density functional method. After comparison of structure stability, we found that the structures of ground-state CN3- and C2N3- are bent chains with a nitrogen atom at either end, whereas when n=3-8, the ground-state clusters show three branches, each with a nitrogen atom located at the end. When n=5-8, the longest branch of CnN3- is polyacetylenelike. When n=5 or 7, the longest branch is connected to the central sp2 carbon in a nonlinear manner. The CnN3- (n=1-8) with an even number of carbon atoms are more stable than those with odd numbers, matching the peak pattern observed in laser-induced mass spectra of CnN3-. The trend of such odd/even alternation is explained based on concepts of bonding characteristics, electron affinities, and incremental binding energies.     

Infrared spectra of the Li+-(H2)n (n=1-3) cation complexes

The Li+-(H2)n n=1-3 complexes are investigated through infrared spectra recorded in the H-H stretch region (3980-4120 cm-1) and through ab initio calculations at the MP2/aug-cc-pVQZ level. The rotationally resolved H-H stretch band of Li+-H2 is centered at 4053.4 cm-1 [a -108 cm-1 shift from the Q1(0) transition of H2]. The spectrum exhibits rotational substructure consistent with the complex possessing a T-shaped equilibrium geometry, with the Li+ ion attached to a slightly perturbed H2 molecule. Around 100 rovibrational transitions belonging to parallel Ka=0-0, 1-1, 2-2, and 3-3 subbands are observed. The Ka=0-0 and 1-1 transitions are fitted by a Watson A-reduced Hamiltonian yielding effective molecular parameters. The vibrationally averaged intermolecular separation in the ground vibrational state is estimated as 2.056 A increasing by 0.004 A when the H2 subunit is vibrationally excited. The spectroscopic data are compared to results from rovibrational calculations using recent three dimensional Li+-H2 potential energy surfaces [Martinazzo et al., J. Chem. Phys. 119, 11241 (2003); Kraemer and Spirko, Chem. Phys. 330, 190 (2006)]. The H-H stretch band of Li+-(H2)2, which is centered at 4055.5 cm-1 also exhibits resolved rovibrational structure. The spectroscopic data along with ab initio calculations support a H2-Li+-H2 geometry, in which the two H2 molecules are disposed on opposite sides of the central Li+ ion. The two equivalent Li+...H2 bonds have approximately the same length as the intermolecular bond in Li+-H2. The Li+-(H2)3 cluster is predicted to possess a trigonal structure in which a central Li+ ion is surrounded by three equivalent H2 molecules. Its infrared spectrum features a broad unresolved band centered at 4060 cm-1.     

A density functional study of YnAl (n=1-14) clusters

The geometries, stabilities, and electronic and magnetic properties of Y(n)Al (n=1-14) clusters have been systematically investigated by using density functional theory with generalized gradient approximation. The growth pattern for different sized Y(n)Al (n=1-14) clusters is Al-substituted Y(n+1) clusters and it keeps the similar frameworks of the most stable Y(n+1) clusters except for Y(9)Al cluster. The Al atom substituted the surface atom of the Y(n+1) clusters for n<9. Starting from n=9, the Al atom completely falls into the center of the Y-frame. The Al atom substituted the center atom of the Y(n+1) clusters to form the Al-encapsulated Y(n) geometries for n>9. The calculated results manifest that doping of the Al atom contributes to strengthen the stabilities of the yttrium framework. In addition, the relative stability of Y(12)Al is the strongest among all different sized Y(n)Al clusters, which might stem from its highly symmetric geometry. Mulliken population analysis shows that the charges always transfer from Y atoms to Al atom in all different sized clusters. Doping of the Al atom decreases the average magnetic moments of most Y(n) clusters. Especially, the magnetic moment is completely quenched after doping Al in the Y(13), which is ascribed to the disappearance of the ininerant 4d electron spin exchange effect. Finally, the frontier orbitals properties of Y(n)Al are also discussed.     

Pseudo-two-dimensional structures (HXYH)3n2H6n (XY = GaN, SiC, GeC, SiSi, or GeGe; n = 1-3): density functional characterization of structures and energetics

Hybrid density functional calculations with effective core potential basis sets are performed for monomeric group 13/15 and group 14/14 analogues of cyclohexane, as well as for three different pseudo-two-dimensional structures that can be formed from expanding one and two concentric rings around the central one (trans-fused chairs, a rolling combination of trans- and cis-fused chairs, and cis-fused boats). Varying contributions from torsional strain, angle strain, electrostatics, and nontraditional H-H hydrogen bonding lead to different orderings and magnitudes of motif energies in the various systems: Homoatomic SiSi and GeGe systems prefer the trans-fused chair alternative and heteroatomic systems GaN, SiC, and GeC prefer the rolling chair. Decomposition of structure energies into characteristic fragment contributions indicates that pseudo-one-dimensional rods of poly(imidogallane) are thermodynamically more stable than any of the pseudo-two-dimensional structures.     

Threshold photoionization and density functional theory studies of the niobium carbide clusters Nb3C(n) (n = 1-4) and Nb4C(n) (n = 1-6)

We have used photoionization efficiency spectroscopy to determine ionization potentials (IP) of the niobium-carbide clusters, Nb3C(n) (n = 1-4) and Nb4C(n) (n = 1-6). The Nb3C2 and Nb4C4 clusters exhibit the lowest IPs for the two series, respectively. For clusters containing up to four carbon atoms, excellent agreement is found with relative IPs calculated using density functional theory. The lowest energy isomers are mostly consistent with the development of a 2 x 2 x 2 face-centered cubic structure of Nb4C4. However, for Nb3C4 a low-lying isomer containing a molecular C2 unit is assigned to the experimental IP rather than the depleted 2 x 2 x 2 nanocrystal isomer. For Nb4C5 and Nb4C6, interpretation is less straightforward, but results indicate isomers containing molecular C2 units are the lowest in energy, suggesting that carbon-carbon bonding is preferred when the number of carbon atoms exceeds the number of metal atoms. A double IP onset is observed for Nb4C3, which is attributed to ionization from the both the lowest energy singlet state and a meta-stable triplet state. This work further supports the notion that IPs can be used as a reliable validation for the geometries of metal-carbide clusters calculated by theory.     

Structures and magnetic properties of CrSi(n) (-) (n = 3-12) clusters: Photoelectron spectroscopy and density functional calculations

Chromium-doped silicon clusters, CrSi(n) (-)(n = 3-12), were investigated with anion photoelectron spectroscopy and density functional theory calculations. The combination of experimental measurement and theoretical calculations reveals that the onset of endohedral structure in CrSi(n) (-) clusters occurs at n = 10 and the magnetic properties of the CrSi(n) (-) clusters are correlated to their geometric structures. The most stable isomers of CrSi(n) (-) from n = 3 to 9 have exohedral structures with magnetic moments of 3-5μ(B) while those of CrSi(10) (-), CrSi(11) (-), and CrSi(12) (-) have endohedral structures and magnetic moments of 1μ(B.).     

Electronic structure of germanium monohydrides Ge(n)H, n = 1-3

Quantum chemical calculations were applied to investigate the electronic structure of germanium hydrides, Ge(n)H (n = 1, 2, 3), their cations, and anions. Computations using a multiconfigurational quasi-degenerate perturbation approach (MCQDPT2) based on complete active space wave functions (CASSCF), multireference perturbation theory (MRMP2), and density functional theory reveal that Ge(2)H has a (2)B(1) ground state with a doublet-quartet gap of approximately 39 kcal/mol. A quasidegenerate (2)A(1) state has been derived to be 2 kcal/mol above the ground state (MCQDPT2/aug-cc-pVTZ). In the case of the cation Ge(3)H(+) and anion Ge(3)H(-), singlet low-lying electronic states are derived, that is, (1)A' and (1)A(1), respectively. The singlet-triplet energy gap is estimated to 6 kcal/mol for the cation. An "Atoms in Molecules" (AIM) analysis shows a certain positive charge on the Ge(n) (n = 1, 2, 3) unit in its hydrides, in accordance with the NBO analysis. The topologies of the electron density of the germanium hydrides are different from that of the lithium-doped counterparts. On the basis of our electron localization function (ELF) analysis, the Ge-H bond in Ge(2)H is characterized as a three-center-two-electron bond. Some key thermochemical parameters of Ge(n)H have also been derived.     

Microhydration of Cs+ ion: a density functional theory study on Cs+-(H2O)n clusters (n=1-10)

Structure, energy enthalpy, and IR frequency of hydrated cesium ion clusters, Cs+-(H2O)n (n=1-10), are reported based on all electron calculations. Calculations have been carried out with a hybrid density functional, namely, Becke's three-parameter nonlocal hybrid exchange-correlation functional B3LYP applying cc-PVDZ correlated basis function for H and O atoms and a split valence 3-21G basis function for Cs atom. Geometry optimizations for all the cesium ion-water clusters have been carried out with several possible initial guess structures following Newton-Raphson procedure leading to many conformers close in energy. The calculated values of binding enthalpy obtained from present density functional based all electron calculations are in good agreement with the available measured data. Binding enthalpy profile of the hydrated clusters shows a saturation behavior indicating geometrical shell closing in hydrated structure. Significant shifts of O-H stretching bands with respect to free water molecule in IR spectra of hydrated clusters are observed in all the hydrated clusters.     

Density functional and Ab initio study of Cr(CO)n (n = 1-6) complexes

Cr(CO)n (n = 1-6) systems were studied for all possible spin states using density functional and high-level ab initio methods to provide a more complete theoretical understanding of the structure of species that may form during ligand dissociation of Cr(CO)6. We carried out geometry optimizations for each system and obtained vibrational frequencies, sequential bond dissociation energies (BDE), and total CO binding energies. We also compared the performance of various DFT functionals. Generally, the ground states of Cr(CO)6, Cr(CO)5, and Cr(CO)4, whose spin multiplicity is a singlet, are in good agreement with both previous theoretical results and currently available experimental data. Calculations on Cr(CO)3, Cr(CO)2, and CrCO provide new findings that the ground state of Cr(CO)3 might be a quintet with C2v symmetry instead of a singlet with C3v symmetry, and the ground state of Cr(CO)2 is not a linear quintet, as suggested by previous DFT calculations, but rather a linear septet. We also found that nonet states of Cr(CO)2 and CrCO display partial C-O bond breakage.     

Theoretical study of mixed silicon-lithium clusters Si(n)Li(p)(+) (n=1-6, p=1-2)

Theoretical study on the structures of neutral and singly charged Si(n)Li(p)((+)) (n=1-6, p=1-2) clusters have been carried out in the framework of the density functional theory (DFT) with the B3LYP functional. The structures of the neutral Si(n)Li(p) and cationic Si(n)Li(p)(+) clusters are found to keep the frame of the corresponding Si(n), Li species being adsorbed at the surface. The localization of the lithium cation is not the same one as that of the neutral atom. The Li(+) ion is preferentially located on a Si atom, while the Li atom is preferentially attached at a bridge site. A clear parallelism between the structures of Si(n)Na(p) and those of Si(n)Li(p) appears. The population analysis show that the electronic structure of Si(n)Li(p) can be described as Si(n)(p)(-)+pLi(+) for the small sizes considered. Vertical and adiabatic ionization potentials, adsorption energies, as well as electric dipole moments and static dipolar polarizabilities, are calculated for each considered isomer of neutral species.     

A density functional theoretical studies on the structures and aromaticities of （CH）n（BCO）6-n （n =0-6）

Density functional theoretical calculations have been made on the electronic structure of （CH）n（BCO）6-n（n = 0-6） at B3LYP/6- 311 ＋ G（d） level. The nuclear-independent chemical shifts （NICS） values calculated using the gauge-including atomic orbitals （GIAO） method were used to assess on the aromaticities of these molecules. The results shows that （CH）n（BCO）6n（n = 0-6） species are aromatic.     

Photoelectron spectroscopy and density functional calculations of CuSi(n)- (n = 4-18) clusters

We conducted a combined anion photoelectron spectroscopy and density functional theory study on the structural evolution of copper-doped silicon clusters, CuSi(n)(-) (n = 4-18). Based on the comparison between the experiments and theoretical calculations, CuSi(12)(-) is suggested to be the smallest fully endohedral cluster. The low-lying isomers of CuSi(n)(-) with n ≥ 12 are dominated by endohedral structures, those of CuSi(n)(-) with n < 12 are dominated by exohedral structures. The most stable structure of CuSi(12)(-) is a double-chair endohedral structure with the copper atom sandwiched between two chair-style Si(6) rings or, in another word, encapsulated in a distorted Si(12) hexagonal prism cage. CuSi(14)(-) has an interesting C(3h) symmetry structure, in which the Si(14) cage is composed by three four-membered rings and six five-membered rings.     

叠氮化合物C6H6-n(N3)n(n=1~6)的密度泛函理论研究

运用密度泛函理论, 在B3LYP/6-31G*水平上, 对叠氮化合物C6H6-n(N3)n(n=1~6)进行理论计算, 并对所得到的几何结构进行了振动频率分析. 计算结果表明, 这些化合物是热力学稳定的. 基于自然键轨道理论, 分析了稳定结构的电荷分布及成键情况. 在不破坏苯环和叠氮基的原则下, 设计等键反应计算了这些化合物的生成热, 结果表明, 标题化合物的生成热都很高, 且随着叠氮基数目的增加而线性增大.     

Stability,Infrared Spectra and Electronic Structures of (ZrO2)n(n=3-6)Clusters:DFT Study

The stability, infrared spectra and electronic structures of (ZrO₂)_n (n=3–6) clusters have been investigated by using density‐functional theory (DFT) at B3LYP/6‐31G* level. The lowest‐energy structures have been recognized by considering a number of structural isomers for each cluster size. It is found that the lowest‐energy (ZrO₂)₅ cluster is the most stable among the (ZrO₂)_n (n=3–6) clusters. The vibration spectra of Zr? O stretching motion from terminal oxygen atom locate between 900 and 1000 cm^?1, and the vibrational band of Zr? O? Zr? O four member ring is obtained at 600–700 cm^?1, which are in good agreement with the experimental results. Mulliken populations and NBO charges of (ZrO₂)_n clusters indicate that the charge transfers occur between 4d orbital of Zr atoms and 2p orbital of O atoms. HOMO‐LUMO gaps illustrate that chemical stabilities of the lowest‐energy (ZrO₂)_n (n=3–6) clusters display an even‐odd alternating pattern with increasing cluster size.     

Density functional study of HO(H2O)n (n = 1–3) clusters

The hydrogen bonding complexes HO(H₂O)_n (n = 1–3) were completely investigated in the present study using DFT and MP2 methods at varied basis set levels from 6‐31++G(d,p) to 6‐311++G(2d,2p). For n = 1 two, for n = 2 two, and for n = 3 five reasonable geometries are considered. The optimized geometric parameters and interaction energies for various complexes at different levels are estimated. The infrared spectrum frequencies and IR intensities of the most stable structures are reported. Finally, thermochemistry studies are also carried out. The results indicate that the formation and the number of hydrogen bonding have played an important role in the structures and relative stabilities of different complexes. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Geometries and magnetisms of the Zr(n) (n=2-8) clusters: the density functional investigations

The geometries, stabilities, and electronic and magnetic properties of small-sized Zr(n) (n=2-8) clusters with different spin configurations were systematically investigated by using density functional approach. Emphasis is placed on studies that focus on the total energies, equilibrium geometries, growth-pattern behaviors, fragmentation energies, and magnetic characteristics of zirconium clusters. The optimized geometries show that the large-sized low-lying Zr(n) (n=5-8) clusters become three-dimensional structures. Particularly, the relative stabilities of Zr(n) clusters in terms of the calculated fragmentation energies and second-order difference of energies are discussed, exhibiting that the magic numbers of stabilities are n=2, 5, and 7 and that the pentagonal bipyramidal D(5h) Zr(7) geometry is the most stable isomer and a nonmagnetic ground state. Furthermore, the investigated magnetic moments confirm that the atomic averaged magnetic moments of the Zr(n) (n not equal to 2) display an odd-even oscillation features and the tetrahedron C(s) Zr(4) structure has the biggest atomic averaged magnetic moment of 1.5 mu(B)/at. In addition, the calculated highest occupied molecular orbital-lowest unoccupied molecular orbital gaps indicate that the Zr(n) (n=2 and 7) clusters have dramatically enhanced chemical stabilities.     

Probing the electronic and structural properties of chromium oxide clusters (CrO3)n(-) and (CrO3)n (n = 1-5): photoelectron spectroscopy and density functional calculations

Photoelectron spectroscopy has been conducted for a series of (CrO3)n(-) (n = 1-5) clusters and compared with density functional calculations. Well-resolved photoelectron spectra were obtained for (CrO3)n(-) (n = 1-5) at 193 nm (6.424 eV) and 157 nm (7.866 eV) photon energies, allowing for accurate measurements of the electron binding energies, low-lying electronic excitations for n = 1 and 2, and the energy gaps. Density functional and molecular orbital theory (CCSD(T)) calculations were performed to locate the ground and low-lying excited states for the neutral clusters and to calculate the electron binding energies of the anionic species. The experimental and computational studies firmly establish the unique low-spin, nonplanar, cyclic ring structures for (CrO3)n and (CrO3)n(-) for n > or = 3. The structural parameters of (CrO3)n are shown to converge rapidly to those of the bulk CrO3 crystal. The extra electron in (CrO3)n(-) (n > or = 2) is shown to be largely delocalized over all Cr centers, in accord with the relatively sharp ground-state photoelectron bands. The measured energy gaps of (CrO3)n exhibit a sharp increase from n = 1 to n = 3 and approach to the bulk value of 2.25 eV at n = 4 and 5, consistent with the convergence of the structural parameters.     

Structure and bonding in cyclic isomers of B2AlH(n)(m) (n = 3-6, m = -2 to +1): a comparative study with B3H(n)(m), BAl2H(n)(m) and Al3H(n)(m)

The structure, bonding and energetics of B(2)AlH(n)(m) (n = 3-6, m = -2 to +1) are compared with corresponding homocyclic boron, aluminum analogues and BAl(2)H(n)(m) using density functional theory (DFT). Divalent to hexacoordinated boron and aluminum atoms are found in these species. The geometrical and bonding pattern in B(2)AlH(4)(-) is similar to that for B(2)SiH(4). Species with lone pairs on the divalent boron and aluminum atoms are found to be minima on the potential energy surface of B(2)AlH(3)(2-). A dramatic structural diversity is observed in going from B(3)H(n)(m) to B(2)AlH(n)(m), BAl(2)H(n)(m) and Al(3)H(n)(m) and this is attributable to the preference of lower coordination on aluminum, higher coordination on boron and the higher multicenter bonding capability of boron. The most stable structures of B(3)H(6)(+), B(2)AlH(5) and BAl(2)H(4)(-) and the trihydrogen bridged structure of Al(3)H(3)(2-) show an isostructural relationship, indicating the isolobal analogy between trivalent boron and divalent aluminum anion.     

Infrared spectroscopy of Li(NH3)n clusters for n=4-7

Infrared spectra of Li(NH3)(n) clusters as a function of size are reported for the first time. Spectra have been recorded in the N-H stretching region for n=4-->7 using a mass-selective photodissociation technique. For the n=4 cluster, three distinct IR absorption bands are seen over a relatively narrow region, whereas the larger clusters yield additional features at higher frequencies. Ab initio calculations have been carried out in support of these experiments for the specific cases of n=4 and 5 for various isomers of these clusters. The bands observed in the spectrum for Li(NH3)(4) can all be attributed to N-H stretching vibrations from solvent molecules in the first solvation shell. The appearance of higher frequency N-H stretching bands for n > or =5 is assigned to the presence of ammonia molecules located in a second solvent shell. These data provide strong support for previous suggestions, based on gas phase photoionization measurements, that the first solvation shell for Li(NH3)(n) is complete at n=4. They are also consistent with neutron diffraction studies of concentrated lithium/liquid ammonia solutions, where Li(NH3)(4) is found to be the basic structural motif.