Ab initiostructures and polarizabilities of sodium clusters

From Infection Clusters to Metal Clusters: Significance of the Lowest Occupied Molecular Orbital (LOMO)

In this paper, the nature of the lowest-energy electrons is detailed. The orbital occupied by such electrons can be termed the lowest occupied molecular orbital (LOMO). There is a good correspondence between the Hückel method in chemistry and graph theory in mathematics; the molecular orbital, which chemists view as the distribution of an electron with a specific energy, is to mathematicians an algebraic entity, an eigenvector. The mathematical counterpart of LOMO is known as eigenvector centrality, a centrality measure characterizing nodes in networks. It may be instrumental in solving some problems in chemistry, and also it has implications for the challenge facing humanity today. This paper starts with a demonstration of the transmission of infectious disease in social networks, although it is unusual for a chemistry paper but may be a suitable example for understanding what the centrality (LOMO) is all about. The converged distribution of infected patients on the network coincides with the distribution of the LOMO of a molecule that shares the same network structure or topology. This is because the mathematical structures behind graph theory and quantum mechanics are common. Furthermore, the LOMO coefficient can be regarded as a manifestation of the centrality of atoms in an atomic assembly, indicating which atom plays the most important role in the assembly or which one has the greatest influence on the network of these atoms. Therefore, it is proposed that one can predict the binding energy of a metal atom to its cluster based on its LOMO coefficient. A possible improvement of the descriptor using a more sophisticated centrality measure is also discussed.

Evolution of the Structural and Electronic Properties of Medium-Sized Sodium Clusters: A Honeycomb-Like Na20 Cluster

Sodium is one of the best examples of a free-electron-like metal and of a certain technological interest. However, an unambiguous determination of the structural evolution of sodium clusters is challenging. Here, we performed an unbiased structure search among neutral and anionic sodium clusters in the medium size range of 10-25 atoms, using the Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) method. Geometries are determined by CALYPSO structure searches, followed by reoptimization of a large number of candidate structures. For most cluster sizes the simulated photoelectron spectra of the lowest-energy structures are in excellent agreement with the experimental data, indicating that the current ground-state structures are the true minima. The equilibrium geometries show that, for both neutral and anionic species, the structural evolution from bilayer structures to layered outsides with interior atoms occurs at n = 16. A novel unprecedented honeycomb-like structure of Na₂₀ cluster with C₃ symmetry is uncovered, which is more stable than the prior suggested structure based on pentagonal structural motifs.

Collectively induced quantum-confined Stark effect in monolayers of molecules consisting of polar repeating units

The electronic structure of terpyrimidinethiols is investigated by means of density-functional theory calculations for isolated molecules and monolayers. In the transition from molecule to self-assembled monolayer (SAM), we observe that the band gap is substantially reduced, frontier states increasingly localize on opposite sides of the SAM, and this polarization in several instances is in the direction opposite to the polarization of the overall charge density. This behavior can be analyzed by analogy to inorganic semiconductor quantum-wells, which, as the SAMs studied here, can be regarded as semiperiodic systems. There, similar observations are made under the influence of a, typically external, electric field and are known as the quantum-confined Stark effect. Without any external perturbation, in oligopyrimidine SAMs one encounters an energy gradient that is generated by the dipole moments of the pyrimidine repeat units. It is particularly strong, reaching values of about 1.6 eV/nm, which corresponds to a substantial electric field of 1.6 × 10(7) V/cm. Close-lying σ- and π-states turn out to be a particular complication for a reliable description of the present systems, as their order is influenced not only by the docking groups and bonding to the metal, but also by the chosen computational approach. In the latter context we demonstrate that deliberately picking a hybrid functional allows avoiding pitfalls due to the infamous self-interaction error. Our results show that when aiming to build a monolayer with a specific electronic structure one can not only resort to the traditional technique of modifying the molecular structure of the constituents, but also try to exploit collective electronic effects.

Density functional investigations on structural and electronic properties of anionic and neutral sodium clusters Na(N) (N = 40-147): comparison with the experimental photoelectron spectra

Density functional calculations have been carried out to obtain low energy equilibrium geometries of anionic and neutral sodium clusters over a wide range of sizes 40 ≤ N ≤ 147, where N is the number of atoms. An exhaustive search for the low energy equilibrium geometries has been carried out. The density of states of the lowest energy geometries are compared with the experimental photoelectron spectra (Huber et al 2009 Phys. Rev. B 80 235425; Kostko et al 2007 Phys. Rev. Lett.98 043401) for N > 41. The agreement between theory and experiment is good for almost all the clusters and the changes in the spectrum with size correlate very well with the changes in the shapes as observed in the evolutionary trend of the ground state geometries.

Electrical response of molecular systems: the power of self-interaction corrected kohn-sham theory

The accurate prediction of electronic response properties of extended molecular systems has been a challenge for conventional, explicit density functionals. We demonstrate that a self-interaction correction (SIC) implemented rigorously within Kohn-Sham theory via the optimized effective potential (OEP) yields polarizabilities close to the ones from highly accurate wave-function-based calculations and exceeding the quality of exact-change OEP. The orbital structure obtained with the OEP-SIC functional and approximations to it are discussed.

First-principles study of intermediate size silver clusters: Shape evolution and its impact on cluster properties

Low-energy isomers of Ag(N) clusters are studied within gradient-corrected density functional theory over the size range of N = 9-20. The candidate conformations are drawn from an extensive structural database created in a recent exploration of Cu(N) clusters [M. Yang et al., J. Chem. Phys. 124, 24308 (2006)]. Layered configurations dominate the list of the lowest-energy isomers of Ag(N) for N < 16. The most stable structures for N > 16 are compact with quasispherical shapes. The size-driven shape evolution is similar to that found earlier for Na(N) and Cu(N). The shape change has a pronounced effect on the cluster cohesive energies, ionization potentials, and polarizabilities. The properties computed for the most stable isomers of Ag(N) are in good agreement with the available experimental data.

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

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

Orbital disproportionation and spin crossover as a pseudo Jahn-Teller effect

It is shown that in systems with electronic half-closed-shell configurations of degenerate orbitals, e(2) and t(3) (which have totally symmetric charge distribution), ground state distortions from high-symmetry geometries may occur due to a strong pseudo Jahn-Teller effect (PJTE) in the excited states, resulting also in a novel phenomenon of PJT-induced spin crossover. There is no JTE neither in the ground state term nor in the excited terms (including degenerate terms) of these configurations but a strong PJT mixing between two excited states [((1)E+(1)A) [cross-filled circle] e and ((2)T(1)+(2)T(2)) [cross-filled circle] e in the e(2) and t(3) cases, respectively] pushes down the lower term to cross the ground state of the undistorted system and to form the global minimum with a distorted geometry. The analysis of the electronic structure of this distorted configuration shows that it is accompanied by orbital disproportionation: instead of proportional population of all degenerate orbitals by one electron each (as in the ground state of the undistorted system that follows Hund's rule), two electrons with opposite spins occupy one orbital, resulting in transformations of the type (e(theta);e(epsilon))-->(e(theta)e(theta)) for e(2) and (t(x);t(y);t(z))-->(t(x);t(x);t(z)) for t(3) systems. Since the two geometry configurations, undistorted and distorted, appertain to different electronic terms that have different spin states, the formation of the global minimum with the distorted configuration is accompanied by a spin crossover. Distinguished from the known spin-crossover phenomenon in some transition metal compounds, the two states with different spin in the PJT-induced spin crossover have also different nuclear configurations, undistorted and distorted, that coexist with a relatively small energy difference. The change of configuration reduces significantly the rate of relaxation between the two states; the relaxation is further reduced by the lower spin-orbital coupling in the light-atom systems as compared with transition metal compounds. This means that there may be systems for which the switch between the two states (in both directions) under perturbations may be observed as a single-molecule phenomenon. Systems with half-closed-shell electronic configurations e(2) and t(3) are available in a variety of molecules from different classes, organic and inorganic; the theory is illustrated here by ab initio calculations for a series of molecular systems, including Si(3), Si(3)C, CuF(3), Na(3), Si(4), Na(4), Na(4) (-), and C(60) (3-), which are in agreement with the experimental data available.

Structure and shape variations in intermediate-size copper clusters

Using extensive, unbiased searches based on density-functional theory, we explore the structural evolution of Cu(n) clusters over the size range n=8-20. For n=8-16, the optimal structures are plateletlike, consisting of two layers, with the atoms in each layer forming a trigonal bonding network similar to that found in smaller, planar clusters (n<or=6). For n=17 and beyond, there is a transition to compact structures containing an icosahedral 13-atom core. The calculated ground-state structures are significantly different from those predicted earlier in studies based on empirical and semiempirical potentials. The evolution of the structure and shape of the preferred configuration of Cu(n), n<or=20, is shown to be nearly identical to that found for Na clusters, indicating a shell-model-type behavior in this size range.

Photoelectron spectroscopy as a structural probe of intermediate size clusters

We examine the utility of photoelectron spectroscopy (PES) as a structural probe of Si(n) (-) in the n=20-26 size range by determining isomers and associated photoelectron spectra from first principles calculations. Across the entire size range, we consistently obtain a good agreement between the theory and experiment [Hoffmann et al., Eur. Phys. J. D 16, 9 (2001)]. We find that PES can almost invariably distinguish between structurally distinct isomers at a given cluster size, but that structurally similar isomers usually cannot be reliably distinguished by PES. For many, but not all, sizes the isomer giving the best match to experiment is the lowest-energy one found theoretically. Thus, combining theory with PES experiments emerges as a useful source of structural information even for intermediate size clusters.

First-principles investigations of the polarizability of small-sized and intermediate-sized copper clusters

Density functional theory calculations are used to compute the dipole polarizabilities of copper clusters. Structures for the clusters are taken from the literature for n = 2-32 and several isomers are used for each cluster size for n < or = 10. The calculated polarizabilities are in good agreement with the prediction of a simple jellium model, but much smaller than experimental observations for n = 9-32 [M. B. Knickelbein, J. Chem. Phys., 120, 10450 (2004)]. To investigate this difference, the calculated polarizabilities are tested for the effects of basis set, electron correlation, and equilibrium geometry for small-size clusters (n = 2-10). These effects are too small to account for the theory-experiment gap. Temperature effects are also studied. Thermal expansion of the clusters leads to very small changes in polarizability. On the other hand, the presence of permanent dipoles in the clusters could account for the experimental observations if the rotational temperature of the clusters were sufficiently low. The potential importance of the cluster dipole moments implies that reliable ground-state structures and experimental temperatures are needed to find quantitative agreement between calculated and observed polarizabilities.

Static dipole polarizability and binding energy of sodium clusters Nan (n=1–10): A critical assessment of all-electron based post Hartree–Fock and density functional methods

A systematic all electron post Hartree-Fock as well as density functional theory (DFT) based calculations for the polarizability and binding energy of sodium metal clusters have been performed and an in-depth analysis of the discrepancy between the experimental and theoretical results is presented. A systematic investigation for the assessment of different DFT exchange-correlation functionals in predicting the polarizability values has also been reported. All the pure DFT functionals have been found to considerably underestimate the calculated polarizability values as compared to the MP2 results. DFT calculations using the full Hartree-Fock exchange along with one-parameter progressive correlation functional have, however, been shown to yield results in good agreement with the MP2 and experimental results. The possible sources of error present in the experimental measurements as well as in the different theoretical methods have also been analyzed. One of the most important conclusions of the present study is that the effect of electron correlation plays a significant role in determining the polarizability of the clusters and the MP2 method can be considered to be one of the most reliable methods for their prediction. It has also been noted that the polarizability value of the lower member clusters (Na2 and Na4) calculated by highly sophisticated methods such as, CCSD and CCSD(T) are found to be very close to the corresponding MP2 values. The polarizability and the binding energy of the clusters are found to be inversely related to each other and their correlation is rationalized by invoking the minimum polarizability principle. A good linear correlation between the polarizability and volume of the cluster has also been found to exist.

Highest electron affinity as a predictor of cluster anion structures

Small clusters have a range of unique physical and chemical phenomena that are strongly size dependent. However, analysis of these phenomena often assumes that thermodynamic equilibrium conditions prevail. We compare experimentally measured and ab initio computed photoelectron spectra of bare and deuterated silicon cluster anions produced in a plasma environment. We find that the isomers detected experimentally are usually not the ground-state isomers, but metastable ones, which indicates that cluster relaxation is strongly limited kinetically by a dwell time that is much shorter than the relaxation time. We show that, under these conditions, the highest electron affinity replaces the traditional lowest total energy as the appropriate criterion for predicting isomer structures. These findings demonstrate that a stringent examination of non-equilibrium effects can be crucial for a correct analysis of cluster properties.