Size- and shape-dependent polarizabilities of sandwich and rice-ball Co(n)Bz(m) clusters from density functional theory

The dipole polarizabilities of Co(n)Bz(m), (n, m = 1-4, m = n, n + 1) clusters are studied by means of an all-electron gradient-corrected density functional theory and finite field method. The dipole moments are relatively large for most of the clusters, implying their asymmetric structures. The total polarizability increases rapidly as cluster size, whereas the average polarizability shows "odd-even" oscillation with relatively large values at (n, n + 1). The polarizabilities exhibit clear shape-dependent variation, and the sandwich structures have systematically larger polarizability and anisotropy than the rice-ball isomers. The dipole polarizabilities are further analyzed in terms of the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap, ionization potential, and electron delocalization volume. We conclude that the polarizability variations are determined by the interplay between the geometrical and electronic properties of the clusters.     

Electrostatic calculation of linear and non-linear optical properties of ice Ih,II, IX and VIII

Macroscopic first- and third-order susceptibilities of ice Ih, ice II, ice IX and ice VIII are calculated using static and frequency-dependent electronic and static vibrational molecular (hyper)polarizabilities at the MP2 level. The molecular properties are in good agreement with experiment and with high-level ab initio calculations. Intermolecular electrostatic and polarization effects due to induced dipoles are taken into account using a rigorous local-field theory. The electric field due to permanent dipoles is used to calculate effective in-crystal (hyper)polarizabilities. The polarizability depends only weakly on the permanent field, but the dipole moment and the hyperpolarizabilities are strongly affected. The calculated linear susceptibility is in good agreement with available experimental data for ice Ih, and the third-order susceptibility for a third harmonic generation experiment is in reasonable agreement with experimental values for liquid water. The molecular vibrational contributions have a small effect on the susceptibilities. The electric properties of a water tetramer are calculated and used to estimate the effect of non-dipolar interactions on the susceptibilities of ice Ih, which are found to be small.     

Calculated spectroscopic and electric properties of the alkali metal-ammonia complexes from Kn-NH3 to Frn-NH3 (n=0,+1)

The newly developed Stuttgart small-core scalar relativistic pseudopotentials for the alkali metals are used to study spectroscopic and electric properties of the heavier alkali metal-ammonia complexes from K(n)-NH(3) to Fr(n)-NH(3) (n=0,+1) at the second-order Moller-Plesset (MP2) and coupled cluster [CCSD(T)] levels of theory. Equilibrium geometries and dissociation energies computed at the MP2 level are in reasonable agreement with their CCSD(T) counterparts, whereas for the dipole polarizabilities MP2 is not performing well overestimating significantly electron correlation effects. The bond distances increase monotonically with increasing mass of the metal atom as relativistic effects are small in these systems. However, the dipole polarizabilities are more sensitive to such effects and we find a decrease in this property from Cs-NH(3) to Fr-NH(3). Combination of CCSD(T) harmonic frequencies and MP2 anharmonic corrections obtained from a perturbative vibrational treatment leads to fundamental frequencies in good agreement with experimental results obtained by Suzer and Andrews [J. Am. Chem. Soc. 109, 300 (1986)]. We also present the results of variational calculations with a three-dimensional vibrational Hamiltonian, making use of CCSD(T) potential energy and electric dipole moment surfaces. Complexation of NH(3) to the metal causes a strong infrared intensification of the symmetric NH(3) stretching mode in the neutral complexes, which is absent in the charged species.     

Electric deflection studies of rhodium clusters

The static electric dipole polarizabilities of rhodium clusters Rhn, n=5-28, have been measured via a molecular beam deflection method. Uniform high-field beam deflections, indicative of induced polarization, were observed for all Rhn except Rh7 and Rh10 which by contrast exhibited beam broadening and anomalously high effective polarizabilities. Analysis of the beam deflection profile of Rh7 indicates that it possesses a permanent dipole moment of 0.24+/-0.02 D. Unlike the other clusters in the n=5-28 size range, the polarizability of Rh10 is observed to decrease with increasing source temperature. We attribute this temperature dependence to paraelectric behavior, suggesting that Rh10 is a fluxional molecule possessing a dipole moment that spatially fluctuates, uncorrelated with overall rotation.     

A theoretical investigation of hyperpolarizability for small Ga(n)As(m) (n + m = 4-10) clusters

In this paper, the second and third order polarizabilities of small Ga(n)As(m) (n + m=4-10) clusters are systematically investigated using the time dependent density functional theory (TDDFT)6-311+G* combined with the sum-over-states method (SOSTDDFT6-311+G*). For the static second order polarizabilities, the two-level term (beta(vec.2)) makes a significant contribution to the beta(vec) for all considered Ga(n)As(m) clusters except for the Ga3As4 cluster. And, for the static third order polarizabilities, the positive channel (gamma(II)) makes a larger contribution to gamma(tot) than the negative channel (gamma(I)). Similar to the cubic GaAs bulk materials, the small Ga(n)As(m) cluster assembled materials exhibit large second order (1 x 10(-6) esu) and third order susceptibilities (5 x 10(-11) esu). The dynamic behavior of beta(-2omega; omega, omega) and gamma(-3omega; omega, omega, omega) show that the small Ga(n)As(m) cluster will be a good candidate of nonlinear optical materials due to the avoidance of linear resonance photoabsorption.     

Electric dipole polarizabilities of copper clusters

The static electric dipole polarizabilities of Cu(9)-Cu(61) have been measured via a molecular beam deflection method. The clusters display per-atom polarizabilities that decrease monotonically with size, from approximately 16 A(3) per atom Cu(9-10) to approximately 5 A(3) (Cu(45-61)). Absent are any discernible discontinuities or odd-even alternations due to electronic shell filling or electron pairing effects. For the smallest clusters, the experimental polarizabilities are approximately 3 times larger than those predicted classically for conducting ellipsoids, and approach the classical values only for clusters containing more than approximately 45 atoms.     

Polarizabilities of heteroaromatic molecules: Azines revisited

Ab initio electron-correlated calculations of the equilibrium geometries, dipole moments, and static dipole polarizabilities are reported for benzene and 12 heteroaromatic six-membered rings obtained from it by aza-substitution. Our geometries and dipole moments agree well with available experimental microwave determinations. The polarizabilities are in reasonable agreement with the fragmentary experimental data available. Uncoupled Hartree-Fock calculations indicate that as much as half the polarizability comes from the σ-electrons. Simple empirical formulas based on atom- and bond-additive models correlate the calculated polarizabilities of 33 five- and six-membered heteroaromatic rings (10 azoles, 10 oxazoles, 13 azines) quite well. The correlation improves significantly if systematic data of uniform quality are used. © 1996 John Wiley & Sons, Inc.     

Dipole polarizabilities of germanium clusters

Dipole polarizabilities of Ge_n clusters with 2–25 atoms are calculated using finite field (FF) method within density functional theory. The dipole moments and polarizabilities of clusters are sensitively dependent on the cluster geometries and electronic structures. The clusters with low symmetry and large HOMO–LUMO gap prefer to large dipole moments. The polarizabilities of the Ge_n clusters increase rapidly in the size range of 2–5 atoms and then fluctuate around the bulk value. The larger HOMO–LUMO gap may lead to smaller polarizability. As compared with the compact structure and diamond structure, the prolate cluster structure corresponds to a larger polarizability.     

Modified Kelvin-Thomson equation considering ion-dipole interaction: comparison with observed ion-clustering enthalpies and entropies

The classical Kelvin-Thomson (CKT) equation does not consider the interaction of condensing molecules with the ions and hence is not able to treat polar and nonpolar molecules differently. The ion-clustering enthalpy and entropy changes predicted by CKT equation for small ions are known to be significantly less negative than those observed. In this paper, we derive a modified Kelvin-Thomson (MKT) equation, which considers the effect of dipole-ion interaction, by taking into account the kinetic energy change of condensing polar ligands as they approach the ions or the extra energy needed for dipole molecules to escape from the ion cluster. The clustering enthalpies and entropies for protonated clusters (H(+)L(n), with L=H(2)O, NH(3), CH(3)OH, and C(5)H(5)N) are calculated based on MKT equation and compared with experimental data. Our calculations indicate that enthalpy values given by MKT equation are in very good agreement with experimental results for small ions (n< or =5) of all four species investigated. MKT predictions appear to be consistent with observed enthalpies for CH(3)OH at n> or =6 and for H(2)O at n=14-25, however, MKT equation cannot reproduce the observed discontinuous transition in enthalpy changes at n=6 for NH(3) and at n=7-13 for H(2)O which is probably associated with the formation of inner shell. The stepwise entropy changes for small ions are 5-15 cal mol(-1) K(-1) more negative when the effect of dipole-ion interaction is considered, which suggests that the ordered structure of the cluster ions can somewhat be accounted for by the dipole-ion interaction term.     

Infrared spectra and ab initio calculations for the Cl--(CH4)n (n = 1-10) anion clusters

In an effort to elucidate their structures, mass-selected Cl--(CH4)n (n = 1-10) clusters are probed using infrared spectroscopy in the CH stretch region (2800-3100 cm(-1)). Accompanying ab initio calculations at the MP2/6-311++G(2df,2p) level for the n = 1-3 clusters suggest that methane molecules prefer to attach to the chloride anion by single linear H-bonds and sit adjacent to one another. These conclusions are supported by the agreement between experimental and calculated vibrational band frequencies and intensities. Infrared spectra in the CH stretch region for Cl--(CH4)n clusters containing up to ten CH4 ligands are remarkably simple, each being dominated by a single narrow peak associated with stretching motion of hydrogen-bonded CH groups. The observations are consistent with cluster structures in which at least ten equivalent methane molecules can be accommodated in the first solvation shell about a chloride anion.     

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.     

Thermally induced polarizabilities and dipole moments of small tin clusters

We study the influence of thermal excitation on the electric susceptibilities for Sn(6) and Sn(7) clusters by molecular beam electric deflection and Monte-Carlo simulations in conjunction with quantum-chemical calculations. At low temperatures (40 K), no field-induced broadening of the Sn(6) and Sn(7) cluster beams are observed, in agreement with vanishing permanent electric dipole moments due to their centro-symmetrical ground states. The electric polarizabilities of Sn(6) and Sn(7), as inferred from the field-induced molecular beam deflection, are in good agreement with the quantum-chemical predictions. At elevated temperatures of 50-100 K, increased polarizabilities of about 2-3 ?(3) are obtained. Also, we found indications of a field-induced beam broadening which points to the existence of permanent dipole moments of about 0.01-0.02 D per atom at higher temperatures. These results cannot be explained by thermal excitations within a harmonic oscillator model, which would yield a temperature-independent polarizability and fluxional, but not permanent, dipole moments. We analyze this behavior by Monte-Carlo simulations in order to compute average temperature-induced electric dipole moments. For that purpose, we developed a novel technique for predicting observables sampled on the quantum-chemical potential energy surface by an umbrella sampling correction of Monte-Carlo results obtained from simulations utilizing an empirical potential. The calculated, fluxional dipole moments are in tune with the observed beam broadenings. The cluster dynamics underlying the polarizability appear to be intermediate between rigid and floppy molecules which leads to the conclusion that the rotational, not the vibrational temperature seems to be the key parameter that determines the temperature dependence of the polarizability.     

The Kohn-Sham density of states and band gap of water: from small clusters to liquid water

Electronic properties of water clusters (H2O)(n), with n=2, 4, 8, 10, 15, 20, and 30 molecules were investigated by sequential Monte Carlo/density-functional theory (DFT) calculations. DFT calculations were carried out over uncorrelated configurations generated by Monte Carlo simulations of liquid water with a reparametrized exchange-correlation functional that reproduces the experimental information on the electronic properties (first ionization energy and highest occupied molecular orbital-lowest unoccupied molecular orbital gap) of the water dimer. The dependence of electronic properties on the cluster size (n) shows that the density of states (DOS) of small water clusters (n>10) exhibits the same basic features that are typical of larger aggregates, such as the mixing of the 3a1 and 1b1 valence bands. When long-ranged polarization effects are taken into account by the introduction of embedding charges, the DOS associated with 3a1 orbitals is significantly enhanced. In agreement with valence-band photoelectron spectra of liquid water, the 1b1, 3a1, and 1b2 electron binding energies in water aggregates are redshifted by approximately 1 eV relative to the isolated molecule. By extrapolating the results for larger clusters the threshold energy for photoelectron emission is 9.6+/-0.15 eV (free clusters) and 10.58+/-0.10 eV (embedded clusters). Our results for the electron affinity (V0=-0.17+/-0.05 eV) and adiabatic band gap (E(G,Ad)=6.83+/-0.05 eV) of liquid water are in excellent agreement with recent information from theoretical and experimental works.     

Investigation of the structures and absorption spectra for some hemicyanine dyes with pyridine nucleus by TD-DFT/PCM approach

Density-functional theory calculations of the Rayleigh optical activities of small isolated polyglycine molecules are reported. Fully extended β-sheet-like conformations of polypeptides of glycine, (Gly)_n (with n=1–5) are considered. After geometry optimizations, dipole moments and dipole polarizabilities (both the mean and the anisotropic components) are calculated using the B3LYP and B3P86 functionals in three basis sets. The polarizabilities are used to analyze the Rayleigh scattering activities and depolarization ratios. The convergence of the average dipole polarizability per monomer is analyzed. The differences in activity and depolarization for Rayleigh scattered radiation between the extended β-sheet-like and the folded -helix-like forms of tetraglycine are analyzed and found to be relevant, suggesting its possible use in experimental characterization.     

Electronic properties of liquid ammonia: a sequential molecular dynamics/quantum mechanics approach

The electronic properties of liquid ammonia are investigated by a sequential molecular dynamics/quantum mechanics approach. Quantum mechanics calculations for the liquid phase are based on a reparametrized hybrid exchange-correlation functional that reproduces the electronic properties of ammonia clusters [(NH3)n; n=1-5]. For these small clusters, electron binding energies based on Green's function or electron propagator theory, coupled cluster with single, double, and perturbative triple excitations, and density functional theory (DFT) are compared. Reparametrized DFT results for the dipole moment, electron binding energies, and electronic density of states of liquid ammonia are reported. The calculated average dipole moment of liquid ammonia (2.05+/-0.09 D) corresponds to an increase of 27% compared to the gas phase value and it is 0.23 D above a prediction based on a polarizable model of liquid ammonia [Deng et al., J. Chem. Phys. 100, 7590 (1994)]. Our estimate for the ionization potential of liquid ammonia is 9.74+/-0.73 eV, which is approximately 1.0 eV below the gas phase value for the isolated molecule. The theoretical vertical electron affinity of liquid ammonia is predicted as 0.16+/-0.22 eV, in good agreement with the experimental result for the location of the bottom of the conduction band (-V 0=0.2 eV). Vertical ionization potentials and electron affinities correlate with the total dipole moment of ammonia aggregates.     

A computational investigation of copper-doped germanium and germanium clusters by the density-functional theory

The geometries, stabilities, and electronic properties of Ge(n) and CuGe(n) (n = 2-13) clusters have been systematically investigated by using density-functional approach. According to optimized CuGe(n) geometries, growth patterns of Cu-capped Ge(n) or Cu-substituted Ge(n+1) clusters for the small- or middle-sized CuGe(n) clusters as well as growth patterns of Cu-concaved Ge(n) or Ge-capped CuGe(n-1) clusters for the large-sized CuGe(n) clusters are apparently dominant. The average atomic binding energies and fragmentation energies are calculated and discussed; particularly, the relative stabilities of CuGe10 and Ge10 are the strongest among all different sized CuGe(n) and Ge(n) clusters, respectively. These findings are in good agreement with the available experimental results on CoGe10- and Ge10 clusters. Consequently, unlike some transition metal (TM)Si12, the hexagonal prism CuGe12 is only low-lying structure; however, the basket-like structure is located as the lowest-energy structure. Different from some TM-doped silicon clusters, charge always transfers from copper to germanium atoms in all different sized clusters. Furthermore, the calculated highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO-LUMO) gaps are obviously decreased when Cu is doped into the Ge(n) clusters, together with the decrease of HOMO-LUMO gaps, as the size of clusters increases. Additionally, the contribution of the doped Cu atom to bond properties and polarizabilities of the Ge(n) clusters is also discussed.     

How important are temperature effects for cluster polarizabilities?

State-of-the-art first-principle all-electron density functional theory calculations on small sodium clusters are performed to study the temperature dependency of their polarizabilities. For this purpose Born-Oppenheimer molecular dynamics simulations with more than 100,000 time steps (>200 ps) are recorded employing gradient corrected functionals in combination with a double-zeta valence polarization basis set. For each cluster 18 trajectories between 50 and 900 K are collected. The cluster polarizabilities are then calculated along these trajectories employing a triple-zeta valence polarization basis set augmented with field-induced polarization functions. The analysis of these calculations shows that the temperature dependency of the sodium cluster polarizabilities varies strongly with cluster size. For several clusters characteristic changes in the polarizability per atom as a function of temperature are observed. It is shown that the inclusion of finite temperature effects resolves the long-standing mismatch between calculated and measured sodium cluster polarizabilities.     

The effect of geometry on cluster polarizability: studies of sodium, copper, and silicon clusters at shape-transition sizes

The electronic properties of Na(16), Cu(16,) and Si(20-28) clusters were calculated using density functional theory with the generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof. These clusters are special, as transitions in cluster shape occur at these sizes in the Na(n), Cu(n), and Si(n) cluster systems, respectively. Low-energy isomers that are comparable in stability, but possess distinctly different shapes, exist at each of these sizes, making these sets of isomers useful as probes of geometrical effects on cluster properties. Results for ionization potentials, electron affinities, and polarizabilities are shown to have a characteristic dependence on cluster shape. An analysis of the results reveals a close relationship between polarizability and cluster volume for all the isomers studied, despite the differences in cluster type and geometry. This relationship accounts for variations in polarizabilities among isomers of the same size, but different shapes, whereas previously published rules relating the polarizability to other cluster properties do not.     

Ab initio study of neutral and charged SinNap(+) (n <or= 6, p <or= 2) clusters

Ab initio calculations in the framework of the density functional theory, with B3LYP functional, are performed to study the lowest-energy isomers of silicon sodium clusters Si(n)Na(p)(+) (n 相似文献   

Size evolution study of "molecular" and "atom-in-cluster" polarizabilities of medium-size gold clusters

A study on static polarizabilities for a family of gold clusters (Au(n), n = 6, 12, 20, 34, 54) is presented. For each cluster, a density functional theory perturbation theory calculation was performed to compute the cluster polarizability and the polarizability of each atom in the cluster using Bader's "quantum theory of atoms in molecules" formalism. The cluster polarizability tensor, α(cluster), is expressed as a sum of the atom-in-molecule tensors, α(cluster)=∑(Ω)α(Ω). A strong quadratic correlation (R(2) = 0.98) in the isotropic polarizability of atoms in the cluster and their distance to the cluster center of mass was observed. The cluster polarizabilities are in agreement with previous calculations.