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.     

Roussin红盐和Roussin黑盐的电子结构

Roussin黑盐簇阴离子及其"元件化合物"Roussin红盐簇阴离子,是固氮酶活性中心福州模型I(网兜状原子簇模型)的模型物.本文用闭壳层CNDO/2(S,D方案)法计算了它们的电子结构.根据计算所得的Mulliken重叠集居,电荷密度,分子轨道能量和轨道特征等数据,对成键性质进行了分析,得出如下主要结论:两种簇阴离子骨架电子的非定域性都比较强,桥硫原子Sb在由红盐形成黑盐的电子转移过程中起施主作用,两种簇阴离子中都存在M-M键,强度与M-Sb键相近,其主要贡献都来源于金属的s,pz,dz2轨道与硫原子的s,pz轨道之间的σ作用,金属d轨道的π作用对整个骨架的成键贡献很小.     

Polarizability and alignment of dielectric nanoparticles in an external electric field: bowls, dumbbells, and cuboids

We employ the coupled dipole method to calculate the polarizability tensor of various anisotropic dielectric clusters of polarizable atoms, such as cuboid-, bowl-, and dumbbell-shaped nanoparticles. Starting from a Hamiltonian of a many-atom system, we investigate how this tensor depends on the size and shape of the cluster. We use the polarizability tensor to calculate the energy difference associated with turning a nanocluster from its least to its most favorable orientation in a homogeneous static electric field, and we determine the cluster dimension for which this energy difference exceeds the thermal energy such that particle alignment by the field is possible. Finally, we study in detail the (local) polarizability of a cubic-shaped cluster and present results indicating that, when retardation is ignored, a bulk polarizability cannot be reached by scaling up the system.     

Origin of the size-dependence of the polarizability per atom in heterogeneous clusters: The case of AlP clusters

An analysis of the atomic polarizabilities α in stoichiometric aluminum phosphide clusters, computed at the MP2 and density functional theory (DFT) levels, the latter using the B3LYP functional, and partitioned using the classic and iterative versions of the Hirshfeld method, is presented. Two sets of clusters are examined: the ground-state Al(n)P(n) clusters (n=2-9) and the prolate clusters (Al(2)P(2))(N) and (Al(3)P(3))(N) (N≤6). In the ground-state clusters, the mean polarizability per atom, i.e., α/2n, decreases with the cluster size but shows peaks at n=5 and at n=7. We demonstrate that these peaks can be explained by a large polarizability of the Al atoms and by a low polarizability of the P atoms in Al(5)P(5) and Al(7)P(7) due to the presence of homopolar bonds in these clusters. We show indeed that the polarizability of an atom within an Al(n)P(n) cluster depends on the cluster size and the heteropolarity of the bonds it forms within the cluster, i.e., on the charges of the atoms. The polarizabilities of the fragments Al(2)P(2) and Al(3)P(3) in the prolate clusters were found to depend mainly on their location within the cluster. Finally, we show that the iterative Hirshfeld method is more suitable than the classic Hirshfeld method for describing the atomic polarizabilities and the atomic charges in clusters with heteropolar bonds, although both versions of the Hirshfeld method lead to similar conclusions.     

Vibrations and thermodynamics of clusters of polycyclic aromatic hydrocarbon molecules: the role of internal modes

The vibrational spectra of clusters of coronene molecules are theoretically calculated using a mixed quantum/classical scheme, each molecule being described by a tight-binding Hamiltonian, the intermolecular forces being provided by explicit Lennard-Jones and point charge sites. The normal modes of vibrations are shown to exhibit significant variations upon clustering. In particular, for large clusters intra- and intermolecular modes tend to mix and fill the mid-infrared range. We also calculate the heat capacity of the (C24H12)8 cluster as a function of temperature, emphasizing the isomerizations that take place during melting. Quantum delocalization effects, as obtained from the Pitzer-Gwinn semiclassical approximation, are important enough to wash out all signatures of the structural transitions on the caloric curve. On the basis of a simple two-state model we estimate that clusters containing about 300 molecules are required for melting to be detected on the caloric curve.     

Water polarizability in condensed phase: ab initio evaluation by cluster approach

The polarizability of a water molecule in liquid is evaluated via ab initio and density functional calculations for water clusters. This work has considerably improved our previous effort [J Chem Phys 1999, 110, 11987] to attain quantitative accuracy for polarizability. The calculations revealed that the water polarizability in the liquid is reduced from that in the gaseous phase by 7-9%. These results suggest significant implications for polarizable water models.     

Theoretical analysis of pyridine protonation in water clusters of increasing size.

The protonation of pyridine in water clusters as a function of the number of water molecules was theoretically analyzed as a prototypical case for the protonation of organic bases. We determined the variation of structural, bonding, and energetic properties on protonation, as well as the stabilization of the ionic species formed. Thus, we used supermolecular models in which pyridine interacts with clusters of up to five water molecules. For each complex, we determined the most stable unprotonated and protonated structures from a simulated annealing at the semi ab initio level. The structures were optimized at the B3LYP/cc-pVDZ level. We found that the hydroxyl group formed on protonation of pyridine abstracts a proton from the ortho-carbon atom of the pyridine ring. The "atoms in molecules" theory showed that this C-H group loses its covalent character. However, starting with clusters of four water molecules, the C-H bond recovers its covalent nature. This effect is associated with the presence of more than one ring between the water molecules and pyridine. These rings stabilize, by delocalization, the negative charge on the hydroxyl oxygen atom. Considering the protonation energy, we find that the protonated forms are increasingly stabilized with increasing size of the water cluster. When zero-point energy is included, the variation follows closely an exponential decrease with increasing number of water molecules. Analysis of the vibrational modes for the strongest bands in the IR spectra of the complexes suggests that the protonation of pyridine occurs by concerted proton transfers among the different water rings in the structure. Symmetric water stretching was found to be responsible for hydrogen transfer from the water molecule to the pyridine nitrogen atom.     

Hirshfeld‐based intrinsic polarizability density representations as a tool to analyze molecular polarizability

In this work, a general scheme to visualize polarizability density distributions is proposed and implemented in a Hirshfeld‐based partitioning scheme. This allows us to obtain easy‐to‐interpret pictorial representations of both total and intrinsic polarizabilities where each point of the density is formed by the contribution of any atom or group of atoms in the molecule. In addition, the procedure used here permits the possibility of removing the size dependence of the electric‐dipole polarizability. Such a development opens new horizons in exploring new applications for the analysis of the molecular polarizability tensor. For instance, this visualization shows which atoms or regions are more polarizable distinguishing, moreover, the fine structure of atoms affected by the vicinity, and might extend the dipole polarizability as a tool for aromaticity studies in polycyclic aromatic hydrocarbons. Additionally, this approach can serve us to assess the methods performance in describing the interaction of electric fields with a molecule and local electron correlation effects in intrinsic polarizabilities. © 2015 Wiley Periodicals, Inc.     

Study of lithium cation in water clusters: based on atom-bond electronegativity equalization method fused into molecular mechanics

We present a potential model for Li(+)-water clusters based on a combination of the atom-bond electronegativity equalization and molecular mechanics (ABEEM/MM) that is to take ABEEM charges of the cation and all atoms, bonds, and lone pairs of water molecules into the intermolecular electrostatic interaction term in molecular mechanics. The model allows point charges on cationic site and seven sites of an ABEEM-7P water molecule to fluctuate responding to the cluster geometry. The water molecules in the first sphere of Li(+) are strongly structured and there is obvious charge transfer between the cation and the water molecules; therefore, the charge constraint on the ionic cluster includes the charged constraint on the Li(+) and the first-shell water molecules and the charge neutrality constraint on each water molecule in the external hydration shells. The newly constructed potential model based on ABEEM/MM is first applied to ionic clusters and reproduces gas-phase state properties of Li(+)(H(2)O)(n) (n = 1-6 and 8) including optimized geometries, ABEEM charges, binding energies, frequencies, and so on, which are in fair agreement with those measured by available experiments and calculated by ab initio methods. Prospects and benefits introduced by this potential model are pointed out.     

Substituent Effect on the Electronic Structure of Sulfines: Molecular Orbital Treatment

The electronic structure and ground state properties of the gaseous sulfine H₂CSO and some of its derivatives were studied at the RHF, MP2, and B3LYP levels. The calculations showed that the Z-isomer is more stable than the E-one and their difference in energy depends on their level of calculation, basis set, and substituent. The factors affecting the isomer stability are the electrostatic interactions, the steric factor, and π-electrons delocalization. The substituent has little effect on the geometry of the CSO moiety but greatly affects its charge distribution and polarizability. The ΔE value of the E- to Z-isomerization process via rotation of the S═O bond was calculated. The substituent has an appreciable effect on both the geometry and energy barrier of isomerization depending on its electronegativity, electrostatic attraction, and effect on π-delocalization over the molecule.     

Fully retarded van der Waals interaction between dielectric nanoclusters

The van der Waals (dispersion) interaction between an atom and a cluster or between two clusters at large separation is calculated by considering each cluster as a point particle, characterized by a polarizability tensor. For the extreme limit of very large separation, the fully retarded regime, one needs to know just the static polarizability in order to determine the interaction. This polarizability is evaluated by including all many-body (MB) intracluster atomic interactions self-consistently. The results of these calculations are compared with those obtained from various alternative methods. One is to consider each cluster as a collection of many atoms and evaluate the sum of two-body interatomic interactions, a common assumption. An alternative method is to include three-body atomic interactions as a MB correction term in the total energy. A comparison of these results reveals that the contribution of the higher-than-three-body MB interactions is always attractive and non-negligible even at such a large separation, in contrast to common assumptions. The procedure employed is quite general and is applicable, in principle, to any shape or size of dielectric cluster. We present numerical results for clusters composed of atoms with polarizability consistent with silica, for which the higher-than-three-body MB correction term can be as high as 42% of the atomic pairwise sum. This result is quite sensitive to the anisotropy and orientation of the cluster, in contrast to the result found in the additive case. We also present a power law expansion of the total van der Waals interaction as a series of n-body interaction terms.     

Evaluation of the molecular polarizability using the IPPP-CLOPPA-INDO/S method. Application to molecules of biological interest

The IPPP-CLOPPA-INDO/S method is introduced to investigate the static molecular polarizability in macromolecules. As an example of application, the polarizability of phospholipidic compounds, with and without the presence of water molecules has been estimated. The IPPP technique was employed to calculate the polarizability of the polar head and the hydrocarbon chains separately to analyze the feasibility of evaluating the total polarizability of the molecule by addition of these two projected results. INDO/S dipole moments of different fragments of the complex molecule were obtained by means of localized molecular orbitals in order to evaluate the charge transfer in the system.     

Can we understand the different coordinations and structures of closed‐shell metal cation‐water clusters?

We present a model potential for studying M(q+)(H(2)O)(n=1,9) clusters where M stands for either Na(+), Cs(+), Ca(2+), Ba(2+), or La(3+). The potential energy surfaces (PES) are explored by the Monte Carlo growth method. The results for the most significant equilibrium structures of the PES as well as for energetics are favorably compared to the best ab initio calculations found in the literature and to experimental results. Most of these complexes have a different coordination number in cluster compared to experimental results in solution or solid phase. An interpretation of the coordination number in clusters is given. In order to well describe the transition between the first hydration sphere and the second one we show that an autocoherent treatment of the electric field is necessary to correctly deal with polarization effects. We also explore the influence of the cation properties (charge, size, and polarizability) on both structures and coordination number in clusters, as well as the meaning of the second hydration sphere. Such an approach shows that the leading term in the interaction energy for a molecule in the second hydration sphere is an electrostatic attraction to the cation and not a hydrogen bond with the water molecules in the first hydration sphere.     

Microhydration of X2 gas (X = Cl, Br, and I): a theoretical study on X2.nH2O clusters (n = 1-8)

Structure and properties of hydrated clusters of halogen gas, X2.nH2O (X = Cl, Br, and I; n = 1-8) are presented following first principle based electronic structure theory, namely, BHHLYP density functional and second-order Moller-Plesset perturbation (MP2) methods. Several geometrical arrangements are considered as initial guess structures to look for the minimum energy equilibrium structures by applying the 6-311++G(d,p) set of the basis function. Results on X2-water clusters (X = Br and I) suggest that X2 exists as a charge separated ion pair, X+delta-X-delta in the hydrated clusters, X2.nH2O (n > or = 2). Though the optimized structures of Cl2.nH2O clusters look like X2.nH2O (X = Br and I) clusters, Cl2 does not exist as a charge separated ion pair in the presence of solvent water molecules. The calculated interaction energy between X2 and solvent water cluster increases from Cl2.nH2O to I2.nH2O clusters, suggesting solubility of gas-phase I2 in water to be a maximum among these three systems. Static and dynamic polarizabilities of hydrated X2 clusters, X2.nH2O, are calculated and observed to vary linearly with the size (n) of these water clusters with correlation coefficient >0.999. This suggests that the polarizability of the larger size hydrated clusters can be reliably predicted. Static and dynamic polarizabilities of these hydrated clusters grow exponentially with the frequency of an external applied field for a particular size (n) of hydrated cluster.     

Bonding study in all-metal clusters containing Al4 units

The nature of the bonding of a series of gas-phase all-metal clusters containing the Al4 unit attached to an alkaline, alkaline earth, or transition metal is investigated at the DFT level using Mulliken, quantum theory of atoms in molecules (QTAIM), and Hirshfeld iterative (Hirshfeld-I) atomic partitionings. The characterization of ionic, covalent, and metallic bonds is done by means of charge polarization and multicenter electron delocalization. This Article uses for the first time Hirshfeld-I multicenter indices as well as Hirshfeld-I based atomic energy calculations. The QTAIM charges are in line with the electronegativity scale, whereas Hirshfeld-I calculations display deviations for transition metal clusters. The Mulliken charges fail to represent the charge polarization in alkaline metal clusters. The large ionic character of Li-Al and Na-Al bonds results in weak covalent bonds. On the contrary, scarcely ionic bonds (Be-Al, Cu-Al and Zn-Al) display stronger covalent bonds. These findings are in line with the topology of the electron density. The metallic character of these clusters is reflected in large 3-, 4- and 5-center electron delocalization, which is found for all the molecular fragments using the three atomic definitions. The previously reported magnetic inactivity (based on means of magnetic ring currents) of the pi system in the Al42- cluster contrasts with its large pi electron delocalization. However, it is shown that the different results not necessary contradict each other.     

Localization measure and maximum delocalization in molecular systems

A mathematically well-defined measure of localization is presented based on Mulliken's orbital populations. It is shown that this quantity equals 1 for core- and lone-pair orbitals, 2 for two-atomic bonds, 6 for benzene rings, etc., and it is applicable for delocalized canonical HF orbitals as well. The definition of this quantity is general in the sense that ab initio MOS with overlapping AO expansion, and semiempirical wave functions using the ZDO approximation as well, can be treated. The localization quantity is essentially “intrinsic,” i.e., no subdivision of the molecule is required. For N-electron wave functions, mean delocalization can be defined. This measure is not invariant to unitary transformations of the one-electron orbitals, characterizing in this way the localized or extended representation of the N-electron wave function. It can be proven, however, that for unitary transformed wave functions a maximum delocalization exists which depends only on the physical (N-electron) properties of the molecule. It is shown that inhomogeneous charge distribution can cause strong electron localization in molecular systems. The delocalization of the canonical Hartree–Fock orbitals, the Parr–Chen circulant orbitals, and the optimum delocalized orbitals is studied by numerical calculations in extended systems.     

DFT studies of the interactions of a graphene layer with small water aggregates

We have investigated the structure, adsorption, electronic states, and charge transfer of small water aggregates on the surface of a graphene layer using density functional theory. Our calculations were focused on water adsorbates containing up to five water molecules interacting with one and both sides of a perfect freestanding sheet. Different orientations of the aggregates with respect to the graphene sites were considered. The results show that the adsorption energy of one water molecule is primarily determined by its orientation, although it is also strongly dependent on the implemented functional scheme. Despite its intrinsic difficulties with dispersion interactions, the Perdew and Wang's exchange-correlation functional may be a viable alternative to investigate the adsorption of large molecular aggregates on a graphene surface. Although water physisorption is expected to occur in the regime of droplets, we found no induced impurity states close to the Fermi level of graphene interacting with small water clusters. In order to investigate the donor/acceptor tendency of the water clusters on graphene, we have performed a Bader charge analysis. Considering the charge transfer mechanism, we have noticed that it should preferentially occur from water to graphene only when the oxygen atom is pointing toward the surface. Otherwise, and in the case of larger adsorbed clusters, charge transfers systematically occur from graphene to water.     

Electrical fluctuations on the surfaces of proteins from hydrodynamic data

We calculate the electrical capacitance on the surfaces of protein molecules from hydrodynamic data of the proteins. Then we estimate the electrical fluctuations (charge, voltage) through the fluctuation-dissipation theorem, which links the electrical capacitance of the system with these fluctuations. From the intrinsic viscosity of the proteins, we estimate the polarizability, which leads to knowledge of the field and dipole fluctuations. From the fitting of the capacitance, polarizability, and electrical fluctuations as a function of the molecular weight of the proteins, we report numerical equations that make it possible to estimate these physical magnitudes for a given protein, knowing the molecular weight. Charge fluctuations are in fractions of unit charge range, voltage fluctuations are in the three-mV-digit range, field fluctuations are in the two-digit mV/nm (10(6) V/m) range, and the dipole moment fluctuations range from two to three digits, times the dipole moment of the water molecule. These surface properties of proteins have not been reported before.     

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.     

The nature of interactions in the ionic crystal of 3-pentenenitrile, 2-nitro-5-oxo, ion(-1), sodium

The hybrid variation -- perturbation many-body interaction energy decomposition scheme has been applied to analyze the physical nature of interactions in the ionic 3-pentenenitrile, 2-nitro-5-oxo, ion(-1), sodium crystal, which can be regarded as a model for a large group of aromatic quaternary nitrogen salts. In the crystal structure the sodium ions and water molecules of adjacent unit cells form a positively charged "inorganic layer" with the sodium ions clustered together along the ab faces with the organic (negative) part in between. This puzzling crystal packing is due to a strong favorable interaction between the water molecule and the sodium ions and a substantial charge transfer from the carbanions that balances out the destabilizing sodium-sodium ion repulsion. Although the majority of cohesion energy of the crystal structure comes from the electrostatic interactions of ions, the resulting net stabilization also depends heavily on the nonadditive delocalization components, due to a counterbalance between the two-body delocalization and exchange effects. The estimated nonadditivity of interactions varies between 12% and 22%.