Polarizabilities Of Clusters Research Articles

Machine Learning for Experimental Reactivity of a Set of Metal Clusters toward C-H Activation.

Understanding the mechanisms of C-H activation of alkanes is a very important research topic. The reactions of metal clusters with alkanes have been extensively studied to reveal the electronic features governing C-H activation, while the experimental cluster reactivity was qualitatively interpreted case by case in the literature. Herein, we prepared and mass-selected over 100 rhodium-based clusters (RhxVyOz- and RhxCoyOz-) to react with light alkanes, enabling the determination of reaction rate constants spanning six orders of magnitude. A satisfactory model being able to quantitatively describe the rate data in terms of multiple cluster electronic features (average electron occupancy of valence s orbitals, the minimum natural charge on the metal atom, cluster polarizability, and energy gap involved in the agostic interaction) has been constructed through a machine learning approach. This study demonstrates that the general mechanisms governing the very important process of C-H activation by diverse metal centers can be discovered by interpreting experimental data with artificial intelligence.

The Effect of Global and Local Chemical Reactivity Descriptors in the Determination of Properties of Transition Metal Clusters

Recently, research on material properties has got lots of attention because of their promising technological applications. In this paper, the author’s focus is on the global and local chemical reactivity descriptors of some transition metal clusters. In addition, the author also include findings of chemical properties with reactivity descriptors. Furthermore, according to Thomas–Fermi approximation and from the exact formulation of Density Functional Theory by Hohenberg and Kohn’s theorem, the author introduce electronegativity and the theory of hardness and softness for further investigation of chemical properties of the clusters. As a part of investigations, the author also introduce the Fukui functions with an emphasis for the determinations of chemical reactivity descriptors. All the results are obtained by theoretical investigation of electronegativity), Chemical potential (), chemical hardness (), and polarizability () of the given transition metal clusters (Cr and Mn). From the results, the author observed that the ionization potential of the clusters increases with decreasing cluster size as the clusters become more stable and tend towards chemical inertness. In conclusion, determination of the reactivity descriptors of the transition metal clusters show results that are in line with previous experimental and theoretical findings.

Static polarizabilities within the generalized Kohn-Sham semicanonical projected random phase approximation (GKS-spRPA).

An analytical implementation of static dipole polarizabilities within the generalized Kohn-Sham semicanonical projected random phase approximation (GKS-spRPA) method for spin-restricted closed-shell and spin-unrestricted open-shell references is presented. General second-order analytical derivatives of the GKS-spRPA energy functional are derived using a Lagrangian approach. By resolution-of-the-identity and complex frequency integration methods, an asymptotic O(N4⁡log(N)) scaling of operation count and O(N3) scaling of storage is realized, i.e., the computational requirements are comparable to those for GKS-spRPA ground state energies. GKS-spRPA polarizabilities are assessed for small molecules, conjugated long-chain hydrocarbons, metallocenes, and metal clusters, by comparison against Hartree-Fock (HF), semilocal density functional approximations (DFAs), second-order Møller-Plesset perturbation theory, range-separated hybrids, and experimental data. For conjugated polydiacetylene and polybutatriene oligomers, GKS-spRPA effectively addresses the "overpolarization" problem of semilocal DFAs and the somewhat erratic behavior of post-PBE RPA polarizabilities without empirical adjustments. The ensemble averaged GKS-spRPA polarizabilities of sodium clusters (Nan for n = 2, 3, …, 10) exhibit a mean absolute deviation comparable to PBE with significantly fewer outliers than HF. In conclusion, analytical second-order derivatives of GKS-spRPA energies provide a computationally viable and consistent approach to molecular polarizabilities, including systems prohibitive for other methods due to their size and/or electronic structure.

Microscopic Model of Radiative Capture Reactions with Cluster Polarizability. Application to 7Be and 7Li

We apply the microscopic three-cluster model developed by the authors to study effects of cluster polarization on the capture reactions 3He(α, γ)7Be, 3He(α, γ) 7Li, 6Li(p, γ)7Be and 6Li(n, γ)7Li. These reactions are of great importance for the astrophysical applications. Thus main attention is paid to the cross section (or the astrophysical S factor) of the reactions at low energies. We also study thoroughly the correlations between the astrophysical S factor of the reactions at zero energy and various quantities associated with the ground state of a compound nucleus.

Probing the size-dependent polarizability of mesoscopic ionic clusters and their induced-dipole interactions.

Mesoscopic clusters composed of oppositely charged particles are ubiquitous in synthetic and biological soft materials. The effective interaction between these clusters is influenced by their polarizability, that is, the ability of their constituent charges to re-arrange in response to an external electrical field. Here, using coarse-grained simulations, we show that the polarizability of electrically neutral ionic clusters decreases as the number of constituent charges increases and/or their Coulombic interaction strength increases for various ion valencies, ion densities, and degrees of cluster boundary hardness. For clusters of random ionomers and their counterions, their polarizability is shown to depend on the number of polymer chains. The variation of the cluster polarizability with the cluster size indicates that throughout the assembly, the induced-dipole interactions between the clusters may be reduced substantially as they acquire more charges while maintaining zero net charge. Under certain conditions, the induced-dipole interactions may become repulsive, as inferred from our simulations with a polarizable solvent. As a result, the dipole-induced related interactions can serve as a counterbalancing force that contributes to the self-limiting aggregation of charge-containing assemblies.

Predicting polarizabilities of silicon clusters using local chemical environments

Calculating polarizabilities of large clusters with first-principles techniques is challenging because of the unfavorable scaling of computational cost with cluster size. To address this challenge, we demonstrate that polarizabilities of large hydrogenated silicon clusters containing thousands of atoms can be efficiently calculated with machine learning methods. Specifically, we construct machine learning models based on the smooth overlap of atomic positions (SOAP) descriptor and train the models using a database of calculated random-phase approximation polarizabilities for clusters containing up to 110 silicon atoms. We first demonstrate the ability of the machine learning models to fit the data and then assess their ability to predict cluster polarizabilities using k-fold cross validation. Finally, we study the machine learning predictions for clusters that are too large for explicit first-principles calculations and find that they accurately describe the dependence of the polarizabilities on the ratio of hydrogen to silicon atoms and also predict a bulk limit that is in good agreement with previous studies.

Adsorption of Organic Compounds by Biomass Chars: Direct Role of Aromatic Condensation (Ring Cluster Size) Revealed by Experimental and Theoretical Studies.

Biomass chars are a major component of the soil environmental black carbon pool and prepared forms are a potentially useful tool in remediation. A function critical to the roles of both environmental and prepared chars is sorption of organic compounds. Char properties known to control sorption include surface area, porosity, functional group composition, and percent aromatic carbon. Here, we show that sorption affinity (but not maximum capacity) of organic compounds is directly related to the degree of condensation of the aromatic fraction. The Dubinin-Ashtakov characteristic sorption energy (EDA, kJ mol-1) of 22 compounds on a thermoseries of bamboo chars correlates strongly with the DP/MAS-13C NMR-determined bridgehead aromatic carbon fraction (χb), which relates to the mean ring cluster size. Density functional theory-computed binding energy (Ebd) for five of the compounds on a representative series of polybenzenoid hydrocarbon open-face sheets also correlates positively with χb, leveling off for rings larger than ∼C55. The Ebd, in turn, correlates strongly with EDA. An increase in Ebd with cluster size is also found for sorption, both monolayer and bilayer, between parallel sheets representing slit micropores. The increasing sorption energy with cluster size is shown to be due to increasing cluster polarizability, which strengthens dispersion forces with the sorbate. The findings underscore a previously overlooked explicit role of aromatic condensation in sorption energy, and illustrate the utility of EDA-Ebd comparison for predicting sorption.

On the Polarizability of a Cluster of Interacting Particles in Polarization Radiation

The study considers diffraction radiation, which is excited when an electron moves near a cluster of two interacting subwavelength particles. The interaction is manifested in the fact that the radiation field from each particle is determined not only by the external field of the electron, but also by the field of the neighboring particle. Based on the obtained expressions for the radiation field, the function of cluster polarizability is determined. It characterizes the cluster response to the field of the electron as a whole. It is interesting that the obtained response function of the cluster to an external field, even in the framework of linear theory, generally depends on the external field itself.

Study of self-interaction errors in density functional predictions of dipole polarizabilities and ionization energies of water clusters using Perdew-Zunger and locally scaled self-interaction corrected methods.

We studied the effect of self-interaction error (SIE) on the static dipole polarizabilities of water clusters modeled with three increasingly sophisticated, non-empirical density functional approximations (DFAs), viz., the local spin density approximation (LDA), the Perdew-Burke-Ernzerhof (PBE) generalized-gradient approximation (GGA), and the strongly constrained and appropriately normed (SCAN) meta-GGA, using the Perdew-Zunger self-interaction-correction (PZ-SIC) energy functional in the Fermi-Löwdin orbital SIC framework. Our results show that while all three DFAs overestimate the cluster polarizabilities, the description systematically improves from LDA to PBE to SCAN. The self-correlation free SCAN predicts polarizabilities quite accurately with a mean absolute error (MAE) of 0.53 bohr3 with respect to coupled cluster singles and doubles (CCSD) values. Removing SIE using PZ-SIC correctly reduces the DFA polarizabilities, but overcorrects, resulting in underestimated polarizabilities in SIC-LDA, SIC-PBE, and SIC-SCAN. Finally, we applied a recently proposed locally scaled SIC (LSIC) method using a quasi self-consistent scheme and using the kinetic energy density ratio as an iso-orbital indicator. The results show that the LSIC polarizabilities are in excellent agreement with mean absolute errors of 0.08 bohr3 for LSIC-LDA and 0.06 bohr3 for LSIC-PBE with most recent CCSD polarizabilities. Likewise, the ionization energy estimates as absolute of highest occupied energy eigenvalue predicted by LSIC are also in excellent agreement with CCSD(T) ionization energies with MAEs of 0.4 eV for LSIC-LDA and 0.06 eV for LSIC-PBE. The LSIC-LDA predictions of ionization energies are comparable to the reported GW ionization energies, while the LSIC-PBE ionization energies are more accurate than the reported GW results.

UV-induced refractive index changes due to silver molecular clusters in photo-thermo-refractive glass

It is shown experimentally that in photo-thermo-refractive glasses the transformation of charged silver subnanosized molecular clusters to neutral state by UV irradiation results in the increase of glass refractive index. Quantum chemistry calculations suggest that such refractive index change is mainly dominated by silver neutral cluster polarizability. In addition to discussion of proposed mechanism, the examples of possible applications are also presented.

PySCF-NAO: An efficient and flexible implementation of linear response time-dependent density functional theory with numerical atomic orbitals

We present an algorithm and its implementation to calculate the propertiesof electronic excitations in molecules and clusters from first principles, using time-dependent density functional theory (TDDFT). The algorithm assumes the use of some localized functions as a basis set to represent the spatial degrees of freedom. It relies on an iterative computation of the induced density according to the Dyson-like equation for the linear response function. The current implementation is built upon so-called numerical atomic orbitals. It is suitable for a wide variety of density functional theory (DFT) software. In this work, we demonstrate TDDFT calculations starting from preceding DFT runs with SIESTA, GPAW and PySCF packages, while a coupling with the other DFT packages such as Fireball and OpenMX is planned. The mentioned packages are capable of performing ab initio molecular dynamics simulations, and the speed of our TDDFT implementation makes feasible to perform a configuration average of the optical absorption spectra. Our code is written mostly in Python language allowing for a quick and compact implementation of most numerical methods and data-managing tasks with the help of NumPy/SciPy libraries and Python intrinsic constructs. Part of the code is written in C and Fortran to achieve a competitive speed in particular sections of the algorithm. Many parts of the current algorithm and implementation are useful in other ab initio methods for electronic excited states, such as Hedin’s GW, Bethe–Salpeter equation and DFT with hybrid functionals. Corresponding proof-of-principles implementations are already part of the code. Program summaryProgram Title:PySCF-NAOProgram Files doi:http://dx.doi.org/10.17632/9wgp6255hn.1Licensing provisions: Apache License, Version 2.0Programming language: Python (2 or 3), Fortran90 and CSupplementary material: We provide the source code and input files to organize example and benchmark calculations discussed in the paper.Nature of the problem: The study of the interaction of photons and charged particles with matter depends upon understanding of electronic excitations in matter. A description of the electronic excitations within time-dependent density functional theory (TDDFT) is popular due to the combination of its reasonable accuracy and its relatively low computational cost. Despite the relative simplicity of TDDFT, its application becomes difficult for quantum systems containing several hundreds of atoms. Such microscopically small systems are relevant in organic electronics, plasmonics and surface science. Therefore, much work has been devoted to the development of adequate electronic structure methods. Moreover, thermal motion of atoms and the presence of solvents affects the properties of electronic excited states in a decisive manner. Modeling of the electronic excited states including the system’s dynamics within the Born–Oppenheimer approximation leads to even stronger efficiency requirements from the corresponding electronic structure methods.Solution method: We discretize the Kohn–Sham Hamiltonian using a basis of numerical atomic orbitals. The induced electronic density is determined in response to a dipolar external perturbation, according to linear response TDDFT, using an iterative algorithm. The method takes advantage of the sparsity generated by the finite support of the numerical atomic orbitals. This allows computing the dynamical polarizability of molecules and clusters containing up to several thousands of atoms.Additional comments including Restrictions and Unusual features: The current algorithm is formulated within the formalism of density response functions. Therefore, one needs to know explicitly an exchange–correlation kernel (second-derivative of energy with respect to variation of the density). The exchange–correlation kernel is analytically known for (semi-)local density functionals, but not for the hybrid density functionals. To date, we implemented only the local density approximation (LDA) for the exchange–correlation kernel to be used with the iterative TDDFT in PySCF-NAO. Spin-restricted formalism for finite systems is covered in the current implementation. Moreover, although our code is prepared to compute the electronic response of all-electron systems, our current implementation of an auxiliary product basis (density-fitting basis) is working best in combination with the use of pseudopotentials.

Structure, stability, catalytic activity, and polarizabilities of small iridium clusters**Project supported by the CNPq, CAPES, and FAPES (Brazilian Agencies).

At the second order Douglas–Kroll–Hess (DKH2) level, the B3PW91 functional in conjunction with the relativistic all-electron basis set of valence triple zeta quality plus polarization functions are employed to compute bond lengths, dissociation energies, vertical ionization potentials, and the highest occupied molecular orbital-lowest unoccupied molecular orbital energy gaps of the small iridium clusters (Irn, n ⩽ 8). These results are compared with the experimental and theoretical data available in the literature. Our results confirm the theoretical predictions made by Feng et al. about the catalytic activities of the Ir4 and Ir6 clusters. From the optimized geometries, DKH2 calculations of static electric mean dipole polarizabilities and polarizability anisotropies are also carried out. It is the first time that the polarizabilities of small iridium clusters have been studied. For n ⩽ 4, the mean dipole polarizabilities per atom present an odd–even oscillatory behavior, whereas from Ir5 to Ir8, they decrease with the cluster size increasing. The dependence of the polarizability anisotropy on the structure symmetry of the iridium cluster is verified.

The effect of UV irradiation on the refractive index modulation in photo-thermo-refractive glasses: Mechanisms and application

It is shown experimentally that in photo-thermo-refractive glasses the transformation of charged silver subnanosized molecular clusters to neutral state by UV irradiation results in the increase of glass refractive index. The increment of the refractive index reaches Δn = 0.76·10−4. Computer simulation has shown that the polarizability of neutral molecular clusters is by 20–40% larger than of charged ones. The reason of this is the increase of electron density and volume of electron density surfaces during the transformation of molecular cluster to the neutral state. The transition molecular cluster from the ground state to the excited state also results in the increase of its polarizability.

Static polarizabilities and optical absorption spectra of boron clusters (n = 2–20, 38 and 40) using first principles

We critically analyze and discuss the optical properties and static polarizabilities of the boron clusters within the framework of the time-dependent density functional theory. Our calculations show the dependence of the static and anisotropic polarizability, dispersion coefficient (C6) and enhancement factor (f) on the shape, size and dimensionality of the clusters. The deviation of the ‘C6’ and ‘f’ from the linearity explains the anisotropic nature of the clusters. The optical absorption occurs in the visible and ultra-violet region. The majority of clusters distinguish by the plasmon-like excitations in the high energy region. This is accompanied by the blue-shift and enhancement in the intensity of spectral lines in the 3D structures. All the optical transitions occur between π or π∗ → σ and σ → π-type of orbital, which is also confirmed from the natural transition orbital. It observes that the optical gap of all the clusters except B4 belongs in the visible part of the spectrum. It also finds that the oscillator strength is suppressed in the visible region with the exception of a couple of small peaks as the low energy transitions are dipole forbidden.

In silico modeling of functionalized graphene oxide-metal cluster conjugates as Raman probe: Raman activity of pyridine

Functionalized graphene – metal nano-conjugates are used as Raman probes, in recent years, for trace level identification of materials having specific Raman active modes. In the present paper, model Raman probes were modeled through conjugation of Au4 and Ag4 clusters with functionalized graphene systems. In silico models of functionalized (5,5)-graphene sheets were designed at the density functional theory (DFT) level through attachments of epoxy, -OH and –NH(CH3)2SH/-CONH(CH3)2SH groups. Model Raman probes were designed through attachment of Au4 and Ag4 clusters to the functional sites. Full geometry optimizations followed by vibrational analysis were carried out to ensure that the designed Raman probes have acceptable geometric characteristics to attach Raman-active molecules to the metal site. Pyridine was used as a test system to investigate the functionality of such model Raman probes through attachment with the metal clusters. It was observed that the chemical effects due to such attachments increase the Raman intensities (RI) of specific Raman modes of pyridine (in-plane symmetric bending (1040 cm-1) and asymmetric stretch-bend (1634 cm-1)), which are too weak in the isolated molecule. Furthermore, the suggested in silico system could provide an important model for basic understanding of RI-enhancements of molecules through increase of the size of the metal clusters, as the observed enhancement was found to be dependent on the polarizability of the metal clusters attached to the molecule of interest.

Structures, Stabilities, Reactivities, and (Hyper)Polarizabilities of Small Gold Clusters

Structures, Stabilities, Reactivities, and (Hyper)Polarizabilities of Small Gold Clusters

Dipole Polarizabilities and Absorption Cross Sections of Two-Particle Nanoclusters of Conductive Homogeneous and Layered Particles with the Degenerate Electron Gas

Frequency dependences of the dipole polarizabilities of clusters consisting of two solid conducting spherical nanoparticles and double-layer metal nanoparticles are investigated versus the geometrical parameters of the system with taking into account the degeneracy of electron gas of its metallic components. It is established that the spectra of the dynamic polarizabilities and absorption cross-sections of clusters have a complex multiresonant structure and strong dependence on the configuration parameters of the cluster, the degree of degeneracy of the metal, and kinetic characteristics of its electron gas. Spectral transformations of the absorption cross-sections of nanoclusters are illustrated under variation of the radii of particles or theirs nuclei, characteristic lengths of the Thomas-Fermi screening, and frequency of electron collisions. The anisotropic nature of absorption of electromagnetic field energy by a cluster is established: it is shown that the value of the absorption cross section depends on the direction of the electric field strength vector relative to the axis of the cluster.

Dipole (hyper)polarizabilities of neutral silver clusters**Project supported by CNPq, CAPES, and FAPES (Brazilian Agencies).

At the Douglas–Kroll–Hess (DKH) level, the B3PW91 functional along with the all-electron relativistic basis sets of valence triple and quadruple zeta qualities are used to determine the structure, stability, and electronic properties of the small silver clusters (Agn, n ⩽ 7). The results presented in this study are in good agreement with the experimental data and theoretical values obtained at a higher level of theory from the literature. Static polarizability and hyperpolarizability are also reported. It is verified that the mean dipole polarizability per atom exhibits an odd-even oscillation and that the polarizability anisotropy is directly related to the cluster shape. In this article, the first study of hyperpolarizabilities of small silver clusters is presented. Except for the monomer, the second hyperpolarizabilities of the silver clusters are significantly larger than those of the copper clusters.

Theoretical studies of the global minima and polarizabilities of small lithium clusters

Lithium clusters Lin (n=1⿿20) have been investigated with density functional theory (DFT) and coupled-cluster (CC) methods. The global minima are located via an improved basin-hopping algorithm. Simulated polarizabilities are in good agreement with the measured data generally. The simulated polarizabilities for Li6, Li12 and Li19 are in reasonable agreement when thermal effects are included, except the Li3 cluster. A linear correlation for the inverse relationship between the CCSD calculated polarizabilities and ionization potential (IP) has been reported to have the linear coefficient of 0.996, which further strengthens our simulations.

Assessment of split-charge equilibration model for development of polarizable force fields

Performance of split-charge equilibration model (SQE) for force field development was tested by computing static and response characteristics of water clusters. Results of the study show that SQE yields reliable results for the molecular electrostatic potential, dipole, and polarizability of clusters of increasing size. Intermolecular charge transfer needs to be considered for hydrogen bonded systems in order to accurately reproduce the dipole versus system size behavior. It was found that the model quantitatively mimics the IR intensities of intermolecular vibrational modes, but fails in the computation of the IR and Raman intensities of intramolecular vibrations. The response of charge distribution to perturbation by point charge is confidently modeled by SQE in the conditions corresponding to the linear-response regime.