Binding Energies Of Clusters Research Articles

Formation and properties of astrophysical carbonaceous dust

The classical theory of grain nucleation suffers from both theoretical and predictive deficiencies. We strive to alleviate these deficiencies in our understanding of dust formation and growth by utilizing an atomistic model of nucleation. Carbon cluster geometries are determined with a set of global minimization algorithms. Using density functional theory, the binding energies of carbon clusters from n=2 to n=99 are then calculated. These energies are used to calculate the critical size and nucleation rate of carbon clusters.We find that the critical cluster size is largely determined by the changes in geometry of the clusters. Clusters with size n=27 and n=8, roughly corresponding to the transition from ring-to-fullerene geometry and chain-to-ring geometry respectively, are the critical sizes across the range of temperature and saturation where nucleation is significant. In contrast to the classical theory, nucleation is enhanced at low-temperatures, and suppressed at high temperatures. These results will be applied to a modified chemical evolution code using results from supernova simulations.

Aun (n = 1,11) Clusters Interacting With Lone-Pair Ligands.

We analyze the pattern of binding energies (BEs) of small Aun clusters (n = 1-7, 11) with lone-pair ligands (L = H2O, SH2, NH3, PH3, PF3, PCl3, and PMe3) employing the density functional theory. We use PBE0 functional with the dispersion correction and scalar relativistic effective core potential. This approach provides correct BEs when compared with benchmark CCSD(T) calculations for Au-L and Au2-L complexes. The pattern of BEs of Aun-L complexes is irregular with BE for Au3 ≈ Au4 > Au2 > Au7 > Au5 > Au11 > Au6 > Au1. Electron affinities (EAs) of Aun clusters exhibit oscillatory pattern with the cluster size. Binding energies of Aun-L complexes are oscillatory as well following EAs of Aun clusters. BEs of odd and even Aun-L complexes were analyzed separately. The bonding mechanism in odd Aun-L complexes is dominated by the lone pair → metal electron donation to the singly occupied valence Aun orbital accompanied by the back-donation. Even Aun clusters create covalent Aun-L bonds with BEs higher than those in odd Aun-L complexes. The BEs pattern and optimized geometries of Aun-L complexes correspond to the picture of creating the gold-ligand bond through the lone pair of a ligand interacting with the singly occupied molecular orbital in odd clusters or lowest unoccupied molecular orbital in even clusters of Aun. Ligands in both odd and even Aun-L complexes form three groups with binding energies that correlate with their ionization energies. The lowest BE is calculated for H2O as a ligand, followed by SH2 and NH3. PX3 ligands exhibit highest BEs.

Ion-induced nucleation of pure biogenic particles.

Atmospheric aerosols and their effect on clouds are thought to be important for anthropogenic radiative forcing of the climate, yet remain poorly understood. Globally, around half of cloud condensation nuclei originate from nucleation of atmospheric vapours. It is thought that sulfuric acid is essential to initiate most particle formation in the atmosphere, and that ions have a relatively minor role. Some laboratory studies, however, have reported organic particle formation without the intentional addition of sulfuric acid, although contamination could not be excluded. Here we present evidence for the formation of aerosol particles from highly oxidized biogenic vapours in the absence of sulfuric acid in a large chamber under atmospheric conditions. The highly oxygenated molecules (HOMs) are produced by ozonolysis of α-pinene. We find that ions from Galactic cosmic rays increase the nucleation rate by one to two orders of magnitude compared with neutral nucleation. Our experimental findings are supported by quantum chemical calculations of the cluster binding energies of representative HOMs. Ion-induced nucleation of pure organic particles constitutes a potentially widespread source of aerosol particles in terrestrial environments with low sulfuric acid pollution.

Accurate calculation of binding energies for molecular clusters – Assessment of different models

In this work we test different strategies to compute high-level benchmark energies for medium-sized molecular clusters. We use the incremental scheme to obtain CCSD(T)/CBS energies for our test set and carefully validate the accuracy for binding energies by statistical measures. The local errors of the incremental scheme are <1kJ/mol. Since they are smaller than the basis set errors, we obtain higher total accuracy due to the applicability of larger basis sets. The final CCSD(T)/CBS benchmark values are ΔE=-278.01kJ/mol for (H2O)10,ΔE=-221.64kJ/mol for (HF)10,ΔE=-45.63kJ/mol for (CH4)10,ΔE=-19.52kJ/mol for (H2)20 and ΔE=-7.38kJ/mol for (H2)10.Furthermore we test state-of-the-art wave-function-based and DFT methods. Our benchmark data will be very useful for critical validations of new methods.We find focal-point-methods for estimating CCSD(T)/CBS energies to be highly accurate and efficient. For foQ-i3CCSD(T)—MP2/TZ we get a mean error of 0.34kJ/mol and a standard deviation of 0.39kJ/mol.

Effects of uniaxial strain on stability and structural evolution of vacancy clusters in copper

The effects of [001] uniaxial strain on the energetics, stable structures, and structural evolution of vacancy clusters with different structure and orientation characteristics in copper have been studied by molecular statics simulation. The dependence of binding energies as functions of strain for different cluster types, including linear, planar, and body types, shows complicated behavior. The binding energies of both linear and planar clusters monotonously vary with the strain from −10% to 10%, while those of body clusters decrease with increasing both tensile and compressive strain. According to the variation of the binding energies, it has been suggested that the linear and planar clusters tend to align parallel (perpendicular) to the strain axis under tensile (compressive) strain. Moreover, both the {001} planar cluster and body cluster become the dominant types when the clusters grow under high strain. Then, a mechanism that the local structure around a vacancy cluster tends to approach the ideal lattice structure without defects and strain has been applied to explain the effects of the uniaxial strain on the relative stability of the vacancy clusters. This tendency is closely tied to the level of the atomic relaxation which can be measured by the average atomic displacement of the nearest-neighbor atoms surrounding the vacancy cluster.

Coupled Cluster Evaluation of the Stability of Atmospheric Acid–Base Clusters with up to 10 Molecules

We investigate the utilization of the domain local pair natural orbital coupled cluster (DLPNO-CCSD(T)) method for calculating binding energies of atmospherical molecular clusters. Applied to small complexes of atmospherical relevance we find that the DLPNO method significantly reduces the scatter in the binding energy, which is commonly present in DFT calculations. For medium sized clusters consisting of sulfuric acid and bases the DLPNO method yields a systematic underestimation of the binding energy compared to canonical coupled cluster results. The errors in the DFT binding energies appear to be more random, while the systematic nature of the DLPNO results allows the establishment of a scaling factor, to better mimic the canonical coupled cluster calculations. Based on the trends identified for the small and medium sized systems, we further extend the application of the DLPNO method to large acid - base clusters consisting of up to 10 molecules, which have previously been out of reach with accurate coupled cluster methods. Using the Atmospheric Cluster Dynamics Code (ACDC) we compare the sulfuric acid dimer formation based on the new DLPNO binding energies with previously published RI-CC2/aug-cc-pV(T+d)Z results. We also compare the simulated sulfuric acid dimer concentration as a function of the base concentration with measurement data from the CLOUD chamber and flow tube experiments. The DLPNO method, even after scaling, underpredicts the dimer concentration significantly. Reasons for this are discussed.

Electronic binding energy and thermal relaxation of Li and LiNa atomic alloying clusters.

We examined the effects of atomic hetero- and under-coordination on the relaxation of the interatomic bonding and electronic binding energy of Li and LiNa cluster alloying using a combination of the bond-order-length-strength correlation and density functional theory calculations. We found that bond nature alteration by heterocoordination, bond relaxation by thermal excitation and atomic coordination contribute intrinsically to the core-level energy shifts with resolution of the binding energy at the atomic sites of terrace edges, facets, and bulk of the LiNa alloy nanoclusters. Our strategies may simplify the complexity of core electron binding energies in analyzing the experimental data of the irregularly coordinating atoms.

Nanostructured copper/copper oxide hybrids: combined experimental and theoretical studies.

With the extensive study of dealloying, copper oxides have been shown to be important members and exhibit huge potential in catalysis, energy transformation and storage fields. In this work, nanostructured copper/copper oxide hybrids were prepared through dealloying the sintered Al85Cu15 alloy and molecular dynamics (MD) simulations as well as calculations based on density functional theory (DFT) were performed to explore the oxidation mechanisms of copper in aqueous electrolytes. Cu/Cu2O/CuO compositions were obtained after immersing the sintered alloys in 20 wt% NaOH solutions under corrosion-free conditions at room temperature. Both X-ray diffraction (XRD) and potentiodynamic polarization results reveal that there exist large differences between the sintered Al85Cu15 alloy and its counterpart cast alloy and the Rietveld simulation analysis as well as MD simulations testify to the inhomogeneous atom distribution in the sintered alloy. DFT studies show that Cun (1 ≤n≤ 9) clusters possess higher surface energies than the Cu(111) surface and the calculated binding energies of the copper clusters and an atomic oxygen (Cun-O) are much higher than that of Cu(111)-O. The low surface diffusivity (Ds) of the clusters at the alloy-electrolyte interface extends their diffusion time, which may be beneficial to the formation and growth of oxide nuclei precursors during the dealloying process. Their microstructures and morphologies characterized by scanning electron microscopy (SEM) and transmission electron microscopy (TEM) show that CuO exists in the form of a nanoplate while Cu2O is a nanoparticle. Nanoporous copper (NPC) obtained by dealloying sintered and cast alloys exists in the form of a bicontinuous ligament-channel structure. This work enriches the dealloying research from both experimental and theoretical aspects.

First-principles studies of multiple trapped impurity C by Ni vacancy and temperature effects in NiAl intermetallics

By using a first-principles pseudopotential method based on the density functional theory and Vienna ab initio Simulation Package (VASP), we investigate the multiple trapping of C by Ni vacancy (VNi) and its temperature effects in NiAl intermetallics. A single C atom is energetically and favorably situated at the Ni-rich octahedron interstitial site that surrounds Ni vacancy, which is shown via calculating the formation energy of C atom in NiAl with Ni vacancy system. Single C atom prefers to interact with neighboring Ni atom and Al atom to form a covalent bond. In NiAl intermetallics, C atoms prefer to be trapped in the Ni vacancy in the sequential way, thus easily forming the CnVNi (n=1, 2, 3, 4) clusters, in which the C4VNi clusters are most energetically favorable. It is interesting to find that when C atoms are trapped by Ni vacancy, all the C atoms themselves prefer to be combined with each other to form a bond, surrounding Ni vacancy. With the C atoms further added, both the charge density and the deformation charge prefer to bind with each other despite the Ni or Al environment and the intrinsic bonding properties of CC bond contain obvious covalent characteristics. Furthermore, using first-principles calculations combined with statistical model, we quantitatively predict point defect concentration as a function of temperature in NiAl intermetallics. It is concluded that the concentration of intrinsic Ni vacancies (VNi) will obviously increase as temperature increases. With the increase of temperature, the concentration of C atoms in the CnVNi cluster is higher than that at the intrinsic position. Besides, it indicates that most of C atoms in NiAl intermetallics are trapped by Ni vacancy, which is due to the larger binding energy of the CnVNi clusters and most of the C atoms are trapped directly by vacancies at room temperature or high temperature to form CnVNi clusters. Since the formation of CnVNi clusters is a process of heat releasing which will further increase the temperature of the NiAl system and produce more and more Ni vacancies, we can conclude that much more vacancies are created as a result of the presence of C impurity in NiAl intermetallics. However, the Ni vacancies exist in the form of CnVNi clusters from our calculation in a certain temperature range (less than 700 K). The existence of this kind of CnVNi cluster can effectively restrain the generations of cracks in the vacancies, which will produce some influences on the mechanical properties of NiAl intermetallic compound. Consequently, our results will provide a valuable reference for understanding the effects of C and vacancy on the mechanical properties of the NiAl intermetallics.

The energy and stability of helium-related cluster in nickel: A study of molecular dynamics simulation

Using molecular dynamics simulation, we investigated the energy and stability of helium-related cluster in nickel. All the binding energies of the He-related clusters are demonstrated to be positive and increase with the cluster sizes. Due to the pre-existed self-interstitial nickel atom, the trapping capability of vacancy to defects becomes weak. Besides, the minimum energy configurations of He-related clusters exhibit the very high symmetry in the local atomistic environment. And for the HeN and HeNV1SIA1 clusters, the average length of He–He bonds shortens, but it elongates for the HeNV1 clusters with helium cluster sizes. The helium-to-vacancy ratio plays a decisive role on the binding energies of HeNVM cluster. These results can provide some excellent clues to insight the initial stage of helium bubbles nucleation and growth in the Ni-based alloys for the Generation-IV Molten Salt Reactor.

Ab initio study of early stage Nb growth on MgO(001)

Using density functional theory calculations we have examined the effects of cluster shape and a neutral O vacancy on the energetics and stability of Nb monomers and clusters on the MgO(001) surface. The relative stability of different monolayer structures is also examined. As found in other cases of metal adsorbates on MgO(001), our results indicate that an O site is the preferred adsorption site for a Nb atom. In addition, O-vacancy sites tend to increase the binding energy of small clusters and thus act as nucleation sites, while the effect of a nearby O vacancy on the binding energy of a Nb cluster is much weaker. In particular, we find that the binding energy for a Nb monomer at an O site (O-vacancy site) is 1.5eV (2.2eV) while the corresponding activation barriers for Nb monomer diffusion are 0.58eV (0.80eV). We also find that, in the absence of O vacancies, the preferred planar structure for tetramers and pentamers is an isotropic (100)-like structure. In contrast, the presence of an O vacancy transforms the isotropic tetramer into an anisotropic (110)-like structure. In addition, due to strain effects as well as strong Nb–Nb interactions, for large clusters (e.g. a complete monolayer) the anisotropic (110) structure is favored over the (100) structure. These results appear to explain recent experimental observations for the dependence of thin-film orientation on deposition conditions. However, we also find that for small (100)-like and (110)-like clusters, three-dimensional (rather than planar) structures are energetically preferred due to the strong Nb–Nb interaction. These results suggest that the pathway to form a coherent (100) or (110) structure during the growth of Nb films on Mg(001) may be relatively complex.

First-principles study of structural and electronic properties of carbon clusters

Using a first-principles method based on density functional theory, together with the generalised gradient approximation, the structures and electronic properties of Cn(n = 2–9) clusters have been determined, and their highest occupied molecular orbital–lowest unoccupied molecular orbital energy gaps and their binding energies have been calculated. The results show that the Cn cluster binding energy, and therefore, the stability of the cluster structure increase monotonically with cluster size n. The cluster energy gap varies in a non-monotonic manner with cluster size, and its range of values indicates that the clusters behave as semiconductors. According to the partial density of states of the carbon atoms, the energy of the s state falls with increasing cluster size, whereas the energy of the p state rises.

Many-Body Basis Set Superposition Effect.

The basis set superposition effect (BSSE) arises in electronic structure calculations of molecular clusters when questions relating to interactions between monomers within the larger cluster are asked. The binding energy, or total energy, of the cluster may be broken down into many smaller subcluster calculations and the energies of these subsystems linearly combined to, hopefully, produce the desired quantity of interest. Unfortunately, BSSE can plague these smaller fragment calculations. In this work, we carefully examine the major sources of error associated with reproducing the binding energy and total energy of a molecular cluster. In order to do so, we decompose these energies in terms of a many-body expansion (MBE), where a "body" here refers to the monomers that make up the cluster. In our analysis, we found it necessary to introduce something we designate here as a many-ghost many-body expansion (MGMBE). The work presented here produces some surprising results, but perhaps the most significant of all is that BSSE effects up to the order of truncation in a MBE of the total energy cancel exactly. In the case of the binding energy, the only BSSE correction terms remaining arise from the removal of the one-body monomer total energies. Nevertheless, our earlier work indicated that BSSE effects continued to remain in the total energy of the cluster up to very high truncation order in the MBE. We show in this work that the vast majority of these high-order many-body effects arise from BSSE associated with the one-body monomer total energies. Also, we found that, remarkably, the complete basis set limit values for the three-body and four-body interactions differed very little from that at the MP2/aug-cc-pVDZ level for the respective subclusters embedded within a larger cluster.

Atomistic simulations of the effect of helium clusters on grain boundary mobility in iron

A series of molecular dynamics simulations was performed in this work to investigate the kinetic interaction between helium clusters and grain boundaries in iron. Helium cluster formation and size distributions were found to be markedly different in the bulk compared to the region of a stationary boundary. Upon reaching a steady-state cluster distribution, the spatial fluctuation of cluster-enriched boundaries was analyzed to determine the grain boundary mobility using the random walk method. Segregated clusters reduced the boundary mobility, the drag effect of clusters increasing as the bulk solute concentration increases. The drag effect was further rationalized by employing Cahn's solute drag model using the effective binding energy of He clusters and the grain boundary diffusivity of a single He atom, their magnitudes having been determined from the segregation level and from monitoring the trajectory of a solute atom in the investigated grain boundaries, respectively. The model is found to provide a satisfactory explanation of the simulation results in the zero velocity limit.

Dispersion- and Exchange-Corrected Density Functional Theory for Sodium Ion Hydration.

A challenge in density functional theory is developing functionals that simultaneously describe intermolecular electron correlation and electron delocalization. Recent exchange-correlation functionals address those two issues by adding corrections important at long ranges: an atom-centered pairwise dispersion term to account for correlation and a modified long-range component of the electron exchange term to correct for delocalization. Here we investigate how those corrections influence the accuracy of binding free energy predictions for sodium-water clusters. We find that the dual-corrected ωB97X-D functional gives cluster binding energies closest to high-level ab initio methods (CCSD(T)). Binding energy decomposition shows that the ωB97X-D functional predicts the smallest ion-water (pairwise) interaction energy and larger multibody contributions for a four-water cluster than most other functionals - a trend consistent with CCSD(T) results. Also, ωB97X-D produces the smallest amounts of charge transfer and the least polarizable waters of the density functionals studied, which mimics the lower polarizability of CCSD. When compared with experimental binding free energies, however, the exchange-corrected CAM-B3LYP functional performs best (error <1 kcal/mol), possibly because of its parametrization to experimental formation enthalpies. For clusters containing more than four waters, "split-shell" coordination must be considered to obtain accurate free energies in comparison with experiment.

A DYNAMICAL POTENTIAL–DENSITY PAIR FOR STAR CLUSTERS WITH NEARLY ISOTHERMAL INTERIORS

We present a potential-density pair designed to model nearly isothermal star clusters (and similar self-gravitating systems) with a central core and an outer turnover radius, beyond which density falls off as $r^{-4}$. In the intermediate zone, the profile is similar to that of an isothermal sphere (density $\rho \propto r^{-2}$), somewhat less steep than the King 62 profile, and with the advantage that many dynamical quantities can be written in a simple closed form. We derive new analytic expressions for the cluster binding energy and velocity dispersion, and apply these to create toy models for cluster core collapse and evaporation. We fit our projected surface brightness profiles to observed globular and open clusters, and find that the quality of the fit is generally at least as good as that for the surface brightness profiles of King 62. This model can be used for convenient computation of the dynamics and evolution of globular and nuclear star clusters.

An accurate and efficient computational protocol for obtaining the complete basis set limits of the binding energies of water clusters at the MP2 and CCSD(T) levels of theory: Application to (H2O)m, m = 2-6, 8, 11, 16, and 17.

We report MP2 and Coupled Cluster Singles, Doubles, and perturbative Triples [CCSD(T)] binding energies with basis sets up to pentuple zeta quality for the (H2O)m=2-6,8 water clusters. Our best CCSD(T)/Complete Basis Set (CBS) estimates are -4.99 ± 0.04 kcal/mol (dimer), -15.8 ± 0.1 kcal/mol (trimer), -27.4 ± 0.1 kcal/mol (tetramer), -35.9 ± 0.3 kcal/mol (pentamer), -46.2 ± 0.3 kcal/mol (prism hexamer), -45.9 ± 0.3 kcal/mol (cage hexamer), -45.4 ± 0.3 kcal/mol (book hexamer), -44.3 ± 0.3 kcal/mol (ring hexamer), -73.0 ± 0.5 kcal/mol (D2d octamer), and -72.9 ± 0.5 kcal/mol (S4 octamer). We have found that the percentage of both the uncorrected (De) and basis set superposition error-corrected (De (CP)) binding energies recovered with respect to the CBS limit falls into a narrow range on either sides of the CBS limit for each basis set for all clusters. In addition, this range decreases upon increasing the basis set. Relatively accurate estimates (within <0.5%) of the CBS limits can be obtained when using the "23, 13" (for the AVDZ set) or the "12, 12" (for the AVTZ, AVQZ, and AV5Z sets) mixing ratio between De and De (CP). These mixing rations are determined via a least-mean-squares approach from a dataset that encompasses clusters of various sizes. Based on those findings, we propose an accurate and efficient computational protocol that can be presently used to estimate accurate binding energies of water clusters containing up to 30 molecules (for CCSD(T)) and up to 100 molecules (for MP2).

Modeling the Charging of Highly Oxidized Cyclohexene Ozonolysis Products Using Nitrate-Based Chemical Ionization.

Several extremely low volatility organic compounds (ELVOCs) formed in the ozonolysis of endocyclic alkenes have recently been detected in laboratory and field studies. These experiments have been carried out with chemical ionization atmospheric pressure interface time-of-flight mass spectrometers (CI-APi-TOF) with nitrate ions as reagent ions. The nitrate ion binds to the detected species through hydrogen bonds, but it also binds very strongly to one or two neutral nitric acid molecules. This makes the measurement highly selective when there is an excess amount of neutral nitric acid in the instrument. In this work, we used quantum-chemical methods to calculate the binding energies between a nitrate ion and several highly oxidized ozonolysis products of cyclohexene. These were then compared with the binding energies of nitrate ion-nitric acid clusters. Systematic configurational sampling of the molecules and clusters was carried out at the B3LYP/6-31+G* and ωB97xD/aug-cc-pVTZ levels, and the final single-point energies were calculated with DLPNO-CCSD(T)/def2-QZVPP. The binding energies were used in a kinetic simulation of the measurement system to determine the relative ratios of the detected signals. Our results indicate that at least two hydrogen bond donor functional groups (in this case, hydroperoxide, OOH) are needed for an ELVOC molecule to be detected in a nitrate ion CI-APi-TOF. Also, a double bond in the carbon backbone makes the nitrate cluster formation less favorable.

Structural, electronic and magnetic properties of small bimetallic zirconium–palladium clusters: Ab initio study

Structural, electronic and magnetic properties of small bimetallic zirconium–palladium clusters, ZrnPdm (n+m⩽5), have been investigated using density functional theory with considering generalized gradient approximation and PBE functional. We have determined the ground state conformations of the bimetallic zirconium–palladium clusters by substitution of Zr and Pd atoms in the optimized lowest energy structures of pure zirconium and palladium clusters. Results reveal that binding energies of the pure Zrn clusters are significantly higher than Pdn clusters with the same number of atoms. Also it is found that binding energy of the Zrn and Pdn clusters increase with growth of the number of consisting atoms in the clusters. Results indicate that, for both Zrn and Pdn clusters the binding energy of planar forms is lower than three-dimensional structures. We have also found that the binding energy of the Pdn clusters increase with substituting one or more Zr atoms in these clusters. We have also studied the HOMO–LUMO energy gap and magnetic moment of the pure and combined Zr and Pd clusters. The energy gap analysis of the pure and combined Pd and Zr clusters show that in generally the HOMO–LUMO gap of the bimetallic ZrnPdm clusters increase in comparison with their corresponding pure clusters with the same number of atoms. According to the spin polarization DFT calculations all of the ZrnPdm (n+m⩽5) have net magnetic moments as instance the Zr2, Pd2 and ZrPd clusters show a total magnetic moment value of 2μB. Some more discussions around charge population and density of states of considered clusters as well as their structural properties have been discussed in the context.

Palladium Clusters Supported on Graphene Monovacancies for Hydrogen Storage

We give a detailed description of the atomic structure and the energetics of H2 adsorption on Pdn (n = 1–4) clusters supported on graphene monovacancies. The large binding energy of small Pdn clusters on these vacancies is a result of strong hybridization between the unsaturated carbon and the Pd atoms, and it further indicates that anchoring avoids migration of Pd clusters on the graphene surface. We found that the binding energy of a single H2 is dependent on both the Pd cluster size and the adsorption site. In general, the H2 bond cleavage is favored by Pd clusters, indicating the formation of metal hydrides. Our calculations predict that the sequential binding energy of H2 decreases from 1.2 to 0.085 eV as a function of the number of adsorbed molecules and that the graphene surface modulates the metal–hydrogen interaction. The analysis of the absorption energies and H2 average bond lengths suggest that the supported Pd4 cluster is a unique species and potential hydrogen storage candidate because it is...