Evolution of the electronic structure of Be clusters

Using a modified symbiotic genetic algorithm approach and many-body interatomic potential derived from first principles, we have calculated equilibrium geometries and binding energies of the ground-state and low-lying isomers of Be clusters containing up to 41 atoms. Molecular-dynamics study was also carried out to study the frequency of occurrence of the various geometrical isomers as these clusters are annealed during the simulation process. For a selected group of these clusters, higher-energy isomers were more often found than their ground-state structures due to large catchment areas. The accuracy of the above ground-state geometries and their corresponding binding energies were verified by carrying out separate ab initio calculations based on molecular-orbital approach and density-functional theory with generalized gradient approximation for exchange and correlation. The atomic orbitals were represented by a Gaussian 6-311G** basis, and the geometry optimization was carried out using the GAUSSIAN 98 code without any symmetry constraint. While the ground-state geometries and their corresponding binding energies obtained from ab initio calculations do not differ much from those obtained using the molecular-dynamics approach, the relative stability of the clusters and the energy gap between the highest occupied and the lowest unoccupied molecular orbitals show significant differences. The energy gaps, calculated using the density-functional theory, show distinct shell closure effects, namely, sharp drops in their values for Be clusters containing 2, 8, 20, 34, and 40 electrons. While these features may suggest that small Be clusters behave free-electron-like and, hence, are metallic, the evolution of the structure, binding energies, coordination numbers, and nearest-neighbor distances do not show any sign of convergence towards the bulk value. We also conclude that molecular-dynamics simulation based on many-body interatomic potentials may not always give the correct picture of the evolution of the structure and energetics of clusters although they may serve as a useful tool for obtaining starting geometries by efficiently searching a large part of the phase space.     

Would the pseudocoordination centre method be appropriate to describe the geometries of lanthanide complexes?

The correct prediction of the ground-state geometries of lanthanide complexes is an important step in the development of efficient light conversion molecular devices (LCMD). Considering this, we evaluate here the capability of semiempirical approaches and ab initio effective core potential (ECP) methodology in reproducing the coordination polyhedron geometries of lanthanide complexes. Initially, we compare the facility of two semiempirical approaches: Pseudocoordination centre method (PCC) and Sparkle model. In the first step, we considered only high-quality crystallographic structures and included 633 complexes, and in the last step, we compare the capability of two semiempirical approaches with ab initio/ECP calculations. Because this last methodology was found to be computationally very demanding, we further used a subset containing 91 high-quality crystallographic structures. A total of 91 ab initio full geometry optimizations were performed. Our results suggest that only the semiempirical Sparkle model (hundreds of times faster) present accuracy similar to what can be obtained by present-day ab initio/ECP full geometry optimization calculations on such lanthanide complexes. In addition, it further indicates that the PCC approach has a poor prediction related to the coordination polyhedron geometries of lanthanide complexes.     

A combination of pseudopotentials and density functionals: Results for Cun, Cun, Agn, and Agn clusters (n ≤ 4)

Structures and binding energies have been calculated for neutral and singly ionized Cu and Ag clusters with up to four atoms. The valence-electron system is treated at the ab initio SCF level; core-valence interaction is accounted for by semi-empirical pseudopotentials, corrected for core polarization; valence correlation is included using a local spin-density-functional approximation, corrected for self-interaction. The results are compared to previous calculations for Li, Na and K clusters, and it is shown that, in spite of the different bulk crystal structure, small group 1a and 1b clusters have many properties in common.     

Geometries and binding energies of small beryllium clusters using various levels of approximations for exchange and correlation: a comparative study

Electronic structure and geometries of small (n≦4) neutral, singly, and doubly ionized clusters of beryllium atoms have been studied using ab initio quantum chemical and local density techniques. In the quantum chemical method the exchange potential is treated exactly in the Hartree-Fock scheme while the correlation correction is incorporated through perturbative procedure. In the density functional approach the exchange and correlation potentials are treated in the local spin density approximation. To facilitate an unambiguous comparison between these methods we have used the same basis functions and numerical procedures. All the investigations yield nearly identical geometries. However, the binding energies using these methods can vary by as much as 2 eV and this variation is comparable to what one obtains using different basis functions.     

Density functional study of the interaction of chlorine atom with small neutral and charged silver clusters

Chlorine adsorption on small neutral, anionic, and cationic silver clusters Ag(n) (n=2-7) has been studied using the PW91PW91 density functional method. It was found that the adsorption of chlorine on the lowest-energy bare clusters does not always produce the lowest-energy complexes. In addition, the binding of chlorine can greatly change the geometries of the silver clusters in some cases. Among various possible adsorption sites, bridge site is energetically preferred for the neutral Ag(n) while top site is energetically more preferred for the anionic Ag(n) with n< or =6. For cationic clusters, adsorptions on bridge and face sites have similar binding energies, which are much larger than those on top sites. Natural bond orbital analyses show that irrespective of charge state, electrons always transfer from silver atoms to adsorbate and silver acts like alkali metals in the interaction with chlorine atom. Significant odd-even alternation patterns in the properties of the complexes have been observed: Even-electron clusters often have higher ionization energies, lower electron affinities, and higher dissociation energies than their odd-electron neighbors. It was also found that chlorine atoms bind more strongly with odd-electron bare clusters than with even-electron bare clusters. These patterns reveal that even-electron clusters are more stable than odd-electron clusters.     

Revisiting small clusters of water molecules

The geometries and relative energies of small clusters of water molecules, (H₂O)_n with 4 ⩽ n ⩽ 8, are reported. For each value of n we have considered the conformations corresponding to the lowest-energy minimum and those in nearby relative minima. Thus we report on six tetramers, four pentamers, six hexanlers, four heptamers, and eigth octamers. The geometrical conformations have been obtained using the Metropolis Monte Carlo method as a minimization technique, where the interaction energy is computed with the MCY potential plus three- and four-body corrections previously discussed. All the reported structures for a given cluster size are found to be close in energy. For the lowest conformation the geometry was optimized with ab initio SCF computations using energy gradients. Our results are compared with previous theoretical studies. We discuss the convergence of the interaction potential for liquid water when expressed in terms of a many-body series expansion.     

Theoretical study of stratospheric relevant anions: nitrate-nitric acid complexes

The ion complexes NO3-(HNO3)n, n = 1-3, have been studied by means of ab initio calculations at the B3LYP/aug-cc-pVTZ level of theory. These systems are the most abundant anionic clusters below approximately 30 km altitude in the stratosphere and also in the upper troposphere. These complexes display short strong hydrogen bonds, which should be considered to explain their abundance in the atmosphere. Equilibrium geometries, harmonic frequencies, relative energies, and thermochemical data have been calculated for these anions for the first time. The calculations indicate small differences of energy in the variation of the two nitrate groups from planarity to an almost perpendicular form for n = 1. Planar geometries are found for n = 2 and 3 to give rise to a highly symmetric C(3h) NO3-(HNO3)3. In all the cases, binding energies close to those of covalent compounds are estimated. When experimental data are available, good correlations are found with our results.     

How computational methods and relativistic effects influence the study of chemical reactions involving Ru‐NO complexes?

Two treatments of relativistic effects, namely effective core potentials (ECP) and all‐electron scalar relativistic effects (DKH2), are used to obtain geometries and chemical reaction energies for a series of ruthenium complexes in B3LYP/def2‐TZVP calculations. Specifically, the reaction energies of reduction ( A ‐ F ), isomerization ( G‐I ), and Cl⁻ negative trans influence in relation to NH₃ ( J ‐ L ) are considered. The ECP and DKH2 approaches provided geometric parameters close to experimental data and the same ordering for energy changes of reactions A ‐ L . From geometries optimized with ECP, the electronic energies are also determined by means of the same ECP and basis set combined with the computational methods: MP2, M06, BP86, and its derivatives, so as B2PLYP, LC‐wPBE, and CCSD(T) (reference method). For reactions A ‐ I , B2PLYP provides the best agreement with CCSD(T) results. Additionally, B3LYP gave the smallest error for the energies of reactions J ‐ L . © 2017 Wiley Periodicals, Inc.     

Small elemental clusters. I. The structures of Be2, Be3, Be4, and Be5

The geometries and energies of beryllium clusters up to Be₅ are examined using ab initio molecular orbital theory. Allowances are made for electron correlation with Møller—Plesset perturbation theory to fourth order. Correlation is found to have a dramatic effect on the relative energies of the several structures examined for Be₄ and Be₅. Furthermore, the effect of d-type basis functions on the correlation energy results in an increased binding energy for the clusters. Be₂ is only weakly bound. For Be₃, the best estimate of the binding energy is 6 kcal/mole for the singlet equilateral triangle. Be₄ is tetrahedral in its ground state and the estimated binding is 56 kcal/mole. The best structure for Be₅ is a singlet trigonal bipyramid, and the binding energy is 88 kcal/mole at the highest level of theory used.     

Density functional studies of LiN and LiN+ (N = 2–30) clusters: Structure,binding and charge distribution

Density functional calculations using B3LYP/6‐311G method have been carried out for small to medium‐sized lithium clusters (Li_N, N = 2–30). The optimized geometries of neutral and singly charged clusters, their binding energies, ionization potential, electron affinity, chemical potential, softness, hardness, highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO–LUMO) gap, and static dipole polarizability have been investigated systematically. In addition, we study the distribution of partial charges in detail using natural population analysis (NPA) in small‐sized clusters (Li_N, N = 2–10), both neutral and cationic, and demonstrate the correlation between symmetry and charge. Uniform distribution of charges in cationic clusters confirms them to be energetically more favorable than the neutral counterparts. Whenever possible, results have been compared with available data. An excellent agreement in every case supports new results as reliable predictions. A careful study of optimized geometries shows that Li₉ is derivable from bulk Li structure, i.e., body centered cubic cell, and higher clusters have optimized shapes derived from this. Further, the turnover form two to three dimensional structure occurs at cluster size N = 6. The quantity α^1/3 (α = polarizability) per atom is found to be broadly proportional to softness (per atom) as well as inverse ionization potential (per atom). The present work forms a sound basis for further study of large‐sized clusters as well as other atomic clusters. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Structural and electronic properties of compound metal clusters

The equilibrium geometries, relative stabilities, and vertical ionization potentials of compound clusters involving Li _n , Na, Mg, and Al atoms have been calculated using ab initio self-consistent field linear combination of atomic orbitals — molecular orbital (SCF-LCAO-MO) method. The exchange energies are calculated exactly using the unrestricted Hartree-Fock (UHF) method whereas the correlation correction is included within the framework of configuration interaction involving pair excitations of valence electrons. While the later correction has no significant effect on the equilibrium geometries of clusters, it is essential for the understanding of relative stabilities. Clusters with even numbers of electrons are found to be more stable than those with odd numbers of electrons regardless of their charge state and atomic composition. The equilibrium geometries of homo-nuclear clusters can be significantly altered by replacing one of its constituent atoms with a hetero-nuclear atom. The role of electronic structure on the geometries and stabilities of compound clusters is discussed.     

Comparison of ab initio,semiempirical, and molecular mechanics calculations for the conformational analysis of ring systems

The potential energy surfaces of four cyclic alkanes have been examined using molecular mechanics, semiempirical, and ab initio methods to determine if they produce mutually consistent results and investigate the source of any errors between the methods. The C₅ ? C₈ cyclic alkanes were chosen since these structures present a finite set of conformations and transition-state geometries and are still within the computational time and memory limits of the quantum mechanical approaches. We also examined several conformations of 1,2-dideoxyribose to determine the effect of heteroatoms on the results for the 5-membered ring. The molecular mechanics and ab initio calculations are consistent in the relative energies and geometries determined for the conformers of all ring systems. While the semiempirical calculations yielded geometries consistent with the other methods (except for 5-membered rings), the relative energies often deviated substantially. A decomposition analysis of the semiempirical and molecular mechanics energies revealed that the disparities are mainly due to errors in the 1-center energies of the semiempirical calculations. The 2-center bonding and nonbonding energies followed reasonable trends for the conformers. The core-repulsion function, however, is suspected of producing anomalies. A minimum in the attractive Gaussian of this term at 2.1 Å for H? H interactions partly explains the propensity of the 5-membered rings to optimize to near planarity (decreasing 1,2-diaxial hydrogen distances to 2.3 Å) and the underestimation of the relative energy of the boat structure of cyclohexane.     

Theoretical studies of organometallic compounds. I. All electron and pseudopotential calculations of Ti(CH3)nCl4 − n (n = 0–4)

The performance of effective core potentials (ECP) and model potentials (MP) has been studied by calculating the geometries and reaction energies of isodesmic reactions for the molecules Ti(CH₃)_nCl_{4 ? n} (n = 0–4) at the Hartree–Fock level of theory. The results are compared with data from all electron calculations and experimental results as far as available. The all electron calculations were performed with a 3-21G basis set from Hehre and a (53321/521/41) basis set from Huzinaga. For the ECP calculations the potentials developed by Hay and Wadt, and for the MP calculations, the model potentials developed by Sakai and Huzinaga, are employed. © 1992 by John Wiley & Sons, Inc.     

Ab initio studies on hydrogen-bonded clusters. I. Linear and cyclic oligomers of hydrogen cyanide

Large-scale ab initio calculations have been performed on linear and cyclic oligomers of hydrogen cyanide molecules applying basis sets ranging from double-zeta to near-Hartree-Fock quality. Equilibrium geometries of linear (HCN)_n clusters with n = 1 to 5 and of cyclic clusters with n = 3, 4 are reported. For most of the complexes complete vibrational analysis has been carried out. In agreement with recent experimental data the linear HCN trimer was found to be more stable than the cyclic trimer. In case of the tetramer linear and cyclic structures are of comparable stability. The structural changes taking place upon polymerization of linear HCN clusters and the convergence of various stage properties to those of the infinite polymer (HCN)_∞ are discussed in detail. The evolution from vibrational spectra of small oligomers to phonon dispersion curves of the infinite polymer is illustrated too.     

Structure, bonding, and linear optical properties of a series of silver and gold nanorod clusters: DFT/TDDFT studies

DFT/TDDFT calculations have been carried out for a series of silver and gold nanorod clusters (Ag(n), Au(n), n = 12-120) whose structures are of cigar-type. Pentagonal Ag(n) clusters with n = 49-121 and hexagonal Au(n) clusters with n = 14-74 were also calculated for comparison. Metal-metal distances, binding energies per atom, ionization potentials, and electron affinities were determined, and their trends with cluster size were examined. The TDDFT calculated excitation energies and oscillator strengths were fit by a Lorentz line shape modification, which gives rise to the simulated absorption spectra. The significant features of the experimental spectra for actual silver and gold nanorod particles are well reproduced by the calculations on the clusters. The calculated spectral patterns are also in agreement with previous theoretical results on different-type Ag(n) clusters. Many differences in the calculated properties are found between the Ag(n) and Au(n) clusters, which can be explained by relativistic effects.     

Relative Stability of Boron Planar Clusters in Diatomic Molecular Model

In the recently introduced phenomenological diatomic molecular model imagining the clusters as certain constructions of pair interatomic chemical bonds, there are estimated specific (per atom) binding energies of small all-boron planar clusters B_n, n = 1–15, in neutral single-anionic and single-cationic charge states. The theoretically obtained hierarchy of their relative stability/formation probability correlates not only with results of previous calculations, but also with available experimental mass-spectra of boron planar clusters generated in process of evaporation/ablation of boron-rich materials. Some overestimation in binding energies that are characteristic of the diatomic approach could be related to differences in approximations made during previous calculations, as well as measurement errors of these energies. According to the diatomic molecular model, equilibrium binding energies per B atom and B–B bond lengths are expected within ranges 0.37–6.26 eV and 1.58–1.65 Å, respectively.     

A comparative study of effective core potential and full-electron calculations in Mo compounds. I. An analysis of topological properties of bond charge distribution

Effective core potential (ECP) and full-electron (FE) calculations for MoS₄^?2, MoO₄^?2, and MoOCl₄ compounds were analyzed. Geometry parameters, binding energies, charge distributions, and topological properties of the electronic density were studied for Mo? L bonds (L = S, O, Cl). Results clearly indicate that those approaches that include valence plus 4s and 4p electrons (ECP2 methods) are able to reproduce the topological properties of Mo? L bonds, charge distributions, and geometries with respect to those obtained by FE methods. ECP methods that consider only the 4d and 5s valence electrons (ECP1) fail in the calculation of molecular properties. The use of 5p functions in ECP1 approaches produces a negative Mulliken charge on Mo. Bader's charges give more consistent results than Mulliken's ones. A new parameter for measuring the degree of ionicity is proposed. © 1994 by John Wiley & Sons, Inc.     

The H and H2 interaction with Pd3Cu,Pd4, and Cu4 fcc (111) clusters: A DFT comparative study

A comparative study of adsorption of H atoms and H₂ molecules on Pd₃Cu, Cu₄, and Pd₄ clusters has been performed through density functional calculations, using the hybrid B3LYP exchange‐correlation functional as implemented in the Gaussian98 program. For Pd atoms the relativistic small‐core effective core potential LANL and LANL2DZ basis set was used and for hydrogen a 6‐31G** basis set was used. The main emphasis is set in the reaction behavior of the different clusters with hydrogen atoms and molecules. We find that full geometry optimization does not appreciably change the metal cluster geometry either for certain reaction modes or the H and H₂ capture parameters, but increases the number of reactive sites of the metal clusters. Also, we found that there is charge transfer competition between H and Cu atoms, which drastically diminishes H₂ adsorption energy, related to the Pd cluster observed value. Edges and threefold sites are the principal hydrogen adsorption sites. Hydrogen has a great mobility over the metal clusters for different minima, especially when Cu is present; many initial pathways end in the same adsorption site. The observed hydrogen adsorption and binding energies are well reproduced by the calculations. Also, the adsorption mechanisms were determined. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Approximate additivity of anion-pi interactions: an ab initio study on anion-pi, anion-pi(2) and anion-pi(3) complexes

We have studied the additivity of the anion-pi interaction using high level ab initio calculations. We have optimized chloride and bromide complexes with one, two and three aromatic units (such as trifluoro-s-triazine and s-triazine). We have analyzed the interaction using the atoms in molecules theory and studied the charge transfer using several methods for deriving atomic charges. The results revealed additivities of both the geometries and the binding energies. We have also proposed a neutral receptor for chloride based on multiple anion-pi interactions. Finally, we have simulated solvent effects within the self-consistent reaction field model.