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.     

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.     

Hartree-Fock energy partitioning in terms of Hirshfeld atoms.

A Hirshfeld decomposition scheme of the Hartree-Fock total molecular energy into atomic energies is presented. The calculations are performed by direct numerical integration and the results are compared for a set of 28 molecules containing different kinds of atoms. The calculated atomic energies show a strong dependency on changes of atomic electron population and hybridization. Linear correlations are found between the energy and the population for H, these being related to the electronegativity of this atom and to the external potential created by the remaining atoms. The proposed energy partitioning scheme appears to be useful for studies such as proton acidity, the anomeric effect and group transferability, and allows atomic virial ratios to be obtained. Finally, the atomic potential energies are found to mimic trends based on exact expressions as well as trends displayed by molecular quantities, thus lending credibility to the partitioning scheme used.     

Atoms-in-molecules in momentum space: a Hirshfeld partitioning of electron momentum densities

A direct application of the Hirshfeld atomic partitioning (HAP) scheme is implemented for molecular electron momentum densities (EMDs). The momentum density contributions of individual atoms in diverse molecular systems are analyzed along with their topographical features and the kinetic energies of the atomic partitions. The proposed p-space HAP-based charge scheme does seem to possess the desirable attributes expected of any atoms in molecules partitioning. In addition to this, the main strength of the p-space HAP is the exact knowledge of the kinetic energy functional and the inherent ease in computing the kinetic energy. The charges derived from HAP in momentum space are found to match chemical intuition and the generally known chemical characteristics such as electronegativity, etc.     

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.     

Local and nonlocal contributions to molecular first-order hyperpolarizability: a Hirshfeld partitioning analysis

Based on first-principles calculations, a decomposition scheme is proposed to investigate the molecular site-specific first-order hyperpolarizability (β) responses by means of Hirshfeld population analysis and finite field method. For a molecule, its β is decomposed into local and nonlocal contributions of individual atoms or groups. The former describes the response within the atomic sphere, while the latter describes the contributions from interatomic charge transfer. This scheme is then applied to six prototypical donor-acceptor (D-A) or D-π-A molecules for which the local and nonlocal hyperpolarizabilities are evaluated based on their MP2 density. Both the local and nonlocal parts exhibit site-specific characteristics, but vary differently with molecular structures. The local part depends mainly on the atomic attributes such as electronegativity and charge state, as well as its location in the molecule, while the nonlocal part relates to the ability and distance of charge delocalization within the molecule, increasing rapidly with molecular size. The proposed decomposition scheme provides a way to distinguish atomic or group contributions to molecular hyperpolarizabilities, which is useful in the molecular design for organic nonlinear optical materials.     

A Monte Carlo study of water clusters

The free energy, internal energy and entropy for water clusters of 8 and 64 molecules have been calculated using the Monte Carlo method and both the Lie-Clementi (C-XII) and Stillinger (ST2) potential functions. Detailed structural data for a cluster of 64 water molecules was also obtained by averaging over a large number of configurations. Average dipole orientations and radial density distributions indicated that individual water molecules were not particularly restricted to fixed orientations and that general ordering tendencies were small.     

Hirshfeld partitioning of the electron density: atomic dipoles and their relation with functional group properties

Atomic dipole moments, derived within the Hirshfeld partitioning of the molecular electron density, have been studied for compounds of the type H-X and Cl-X, for a series of functional groups X frequently encountered in organic molecules. In the case of the H-X compounds, the component of the atomic dipole moment on H along the axis connecting H with the central atom in X is found to be linearly correlated with the electronegativity of X, the hardness of X playing no significant role. In the case of the Cl-X compounds, the situation is less clear. However, evidence seems to point to the conclusion that for these compounds, also the group hardness plays an important role.     

Atomic charges,dipole moments,and Fukui functions using the Hirshfeld partitioning of the electron density

In the Hirshfeld partitioning of the electron density, the molecular electron density is decomposed in atomic contributions, proportional to the weight of the isolated atom density in the promolecule density, constructed by superimposing the isolated atom electron densities placed on the positions the atoms have in the molecule. A maximal conservation of the information of the isolated atoms in the atoms-in-molecules is thereby secured. Atomic charges, atomic dipole moments, and Fukui functions resulting from the Hirshfeld partitioning of the electron density are computed for a large series of molecules. In a representative set of organic and hypervalent molecules, they are compared with other commonly used population analysis methods. The expected bond polarities are recovered, but the charges are much smaller compared to other methods. Condensed Fukui functions for a large number of molecules, undergoing an electrophilic or a nucleophilic attack, are computed and compared with the HOMO and LUMO densities, integrated over the Hirshfeld atoms in molecules.     

F-structure of polyhedral water clusters

Energy and entropy characteristics of the F-structures of polyhedral water clusters containing tetragonal, pentagonal, and hexagonal faces with the intermolecular potential ST2 are studied.Institute of Thermal Physics, Ural Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 34, No. 4, pp. 77–82, July–August, 1993.Translated by L. Smolina     

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.     

Electric dipole polarizabilities and C6 dipole-dipole dispersion coefficients for sodium clusters and C60

The frequency-dependent polarizabilities of closed-shell sodium clusters containing up to 20 atoms have been calculated using the linear complex polarization propagator approach in conjunction with Hartree-Fock and Kohn-Sham density functional theories. In combination with polarizabilities for C(60) from a previous work [J. Chem. Phys. 123, 124312 (2005)], the C(6) dipole-dipole dispersion coefficients for the metal-cluster-to-cluster and cluster-to-buckminster-fullerene interactions are obtained via the Casimir-Polder relation [Phys. Rev. 73, 360 (1948)]. The B3PW91 results for the polarizability of the sodium dimer and tetramer are benchmarked against coupled cluster calculations. The error bars of the reported theoretical results for the C(6) coefficients are estimated to be 5%, and the results are well within the error bars of the experiment.     

Nitroxide partitioning between styrene and water

Research into nitroxide‐mediated radical polymerization (NMRP) performed in emulsions and miniemulsions has progressed significantly over the past several years. However, our knowledge of the conditions during polymerization (e.g., the nitroxide concentrations in the aqueous and organic phases) is incomplete, and as such we have yet to achieve a clear understanding of the mechanisms involved in these processes. To better understand the conditions present in heterogeneous NMRP, we measured the partition coefficients of 2,2,6,6‐tetramethylpiperidinyl‐1‐oxy (TEMPO), 4‐hydroxy‐TEMPO, and 4‐amino‐TEMPO between styrene and water from 25 to 135 °C. Experiments were performed in a 250‐mL Parr reactor that was equipped for the simultaneous sampling of the aqueous and organic phases. Aqueous‐phase and organic‐phase nitroxide concentrations were measured with ultraviolet–visible spectrophotometry. Experiments were also performed at 135 °C in the presence of hexadecane (costabilizer), polystyrene, and sodium dodecylbenzenesulfonate (surfactant) to determine the effects of the miniemulsion polymerization recipe ingredients on the partitioning of TEMPO and 4‐hydroxy‐TEMPO. On the basis of the measured partition coefficients (expressed as the ratio of the nitroxide concentration in the organic phase to the nitroxide concentration in the aqueous phase), 4‐hydroxy‐TEMPO was the most hydrophilic of the nitroxides investigated, followed by 4‐amino‐TEMPO and TEMPO. Hexadecane, polystyrene, and sodium dodecylbenzenesulfonate did not have a significant influence on the partitioning of these nitroxides at 135 °C. Experiments with ethylbenzene instead of styrene demonstrated that thermally generated radicals were not responsible for the observed temperature effects on the measured partition coefficients. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 1081–1089, 2001     

A molecular dynamics study of small water clusters comparing two flexible models for water

We report results from a molecular dynamics study of small water clusters, (H₂O) _n=2,3,4,6,8, comparing the recent polarizable, dissociable (PD) model of Halley et al. with the central force Stillinger-Rahman (SR) model. Dynamics calculations in the microcanonical ensemble quantified short-time averaged temperatures and RMS bond length fluctuations, which, in combination with simulated thermal quenching, identified structures and structural and phase changes of the clusters. Both models generally pointed to similar global minimum energy configurations, but local minima configurations, relative energies, and RMS bond length fluctuations varied more significantly. The PD model, with its incorporation of many-body effects, more accurately reproduced the structural features of clusters predicted from ab initio calculations, although it over-estimated the binding energies. Solid-like, pre-melting, and liquid-like states were identified based upon RMS bond length fluctuations for the O-O, O-H and H-H pairs. The SR and PD models yielded very similar trends in melting temperature as a function of cluster size. This suggests that general trends in the melting phenomenon do not depend strongly upon details of the models. The melting temperatures for the dimer and tetramer closely resembled the bulk melting temperature, while those for other sizes were considerably lower.     

Ion solvation in water clusters

We describe here molecular dynamics computer simulations performed to study the solvation of ions (Cl^? and Na⁺) in water clusters. Our simulations show that the calculated structure and dynamics of the clusters is very sensitive to the potential model which is used to describe the interactions. From the comparison with thermodynamic data and data from the photoelectron spectra we conclude that in Cl^?(H₂O)_n (n≤20) clusters the ion is located on the surface of the cluster.     

Proton mobility in water clusters

Proton mobility in water occurs quickly according to the so-called Grotthuss mechanism. This process and its elementary reaction steps can be studied in great detail by applying suitable mass spectrometric methods to ionic water clusters. Careful choice of suitable core ions in combination with analysis of cluster size trends in hydrogen/deuterium isotope exchange rates allows for detailed insights into fascinating dynamical systems. Analysis of the experiments has been promoted by extensive and systematic quantum chemical model calculations. Detailed low-energy mechanistic pathways for efficient water rearrangement and proton transfer steps, in particular cases along short preformed "wires" of hydrogen bonds, have been identified in consistency with experimental findings.     

A variational method for calculating dynamic polarizabilities

We investigate whether or not a previously proposed variation-perturbation method for calculating static polarizabilities can be used also to calculate dynamic polarizabilities. We find that the method can be used for frequencies below the first excitation frequency of the system. By amending and supplementing the procedures for solving the second-order equations we can obtain the same accuracy for dynamic polarizabilities as in the previous procedure for static polarizabilities.     

Hydrogen–hydrogen interaction in planar biphenyl: A theoretical study based on the interacting quantum atoms and Hirshfeld atomic energy partitioning methods

The nature of H‐H interaction between ortho‐hydrogen atoms in planar biphenyl is investigated by two different atomic energy partitioning methods, namely fractional occupation iterative Hirshfeld (FOHI) and interacting quantum atoms (IQA), and compared with the traditional virial‐based approach of quantum theory of atoms in molecules (QTAIM). In agreement with Bader's hypothesis of H? H bonding, partitioning the atomic energy into intra‐atomic and interatomic terms reveals that there is a net attractive interaction between the ortho‐hydrogens in the planar biphenyl. This falsifies the classical view of steric repulsion between the hydrogens. In addition, in contrast to the traditional QTAIM energy analysis, both FOHI and IQA show that the total atomic energy of the ortho‐hydrogens remains almost constant when they participate in the H‐H interaction. Although, the interatomic part of atomic energy of the hydrogens plays a stabilizing role during the formation of the H? H bond, it is almost compensated by the destabilizing effects of the intra‐atomic parts and consequently, the total energy of the hydrogens remains constant. The trends in the changes of intra‐atomic and interatomic energy terms of ortho‐hydrogens during H? H bond formation are very similar to those observed for the H₂ molecule. © 2014 Wiley Periodicals, Inc.     

Ionization of sodium in water clusters

Structures of Na(H₂O)_n and Na⁺(H₂O)_n clusters with n = 1?6, 19, and 28 are determined in the second order of the Møller-Plesset perturbation theory with the use of extended atomic basis set 6–31++G^**. It is found that when the number of molecules is sufficient for the formation of two solvation shells around sodium, a continuous hydrogen-bond network is formed in both neutral and charged clusters, and the orientation of each molecule is determined by the balance between interactions with the neighboring water molecules and with the field of the central particle. In the cations, this field is stronger, and up to the third solvation shell, molecules have a predominant orientation with respect to sodium. In the neutral clusters, with an increase in the number of water molecules, the maximum of the electron density distribution of the highest occupied molecular orbital becomes more distant from the sodium nucleus, being shifted toward the cluster surface. The energy of this orbital accordingly decreases in absolute value approaching 22 kcal/mol inmicroparticles. In the charged clusters, the distribution of the positive charge generally correlates with the character of the highest occupied orbital in the neutral systems, so that with an increase in the number of molecules, the atomic charge of sodium decreases and tends to zero as n → ∞. The ionization potential of sodium changes in inverse proportion to the linear size of the cluster, and should not exceed 1.1 eV in watermicroparticles.