Quantum Monte Carlo determination of electronic and structural properties of Sin clusters (n <= 20)

Introducing hafnium to atomically small- and medium-sized tin clusters (HfSnn0/-/2- (n = 4-17)): A computational investigation of geometrical and growth behavior, spectral properties, electronic configuration and thermochemistry

The global and local minimum configurations of single Hf atom doped Sn clusters are conducted via density function theory (DFT) combined with artificial bee colony algorithm (ABCluster). Furthermore, DFT method is also used to systematically investigate on their structural growth evolution, spectral and electronic information, thermochemical properties following the size of tin clusters doped Hf atom. Structurally, the ground-state geometries of neutral, anion and di-anion are discovered that, from n = 4, the number of Sn atoms in cluster, HfSnn0/-/2- adsorb additional Sn atom on the prior architecture one by one until forming n = 17 for HfSnn-10/-, as well as forming n = 16 for HfSnn-12-. And for the HfSn110/- and HfSn102- as beginning the species veritably develop sealed architectures. The strongest vibrational modes of sealed nanoclusters are stretching modes of Hf atom with infrared actives and breathing modes of the Sn cage framework with Raman actives, respectively. The natural population analysis (NPA) elucidates the stronger relationship between the Hf atoms and the tin frameworks in sealed clusters than that in unsealed clusters. The results of thermochemical properties, molecular orbital shell (MOs), adaptive natural density partitioning (AdNDP) and ultraviolet visible absorption spectrum (UV-Vis) indicate that, the HfSn16 with high symmetry of Td exhibits thermochemical stability and optoelectronic properties, which is utilized potentially as zero-dimensional unit of self-assembling fluorescent nanomaterials.

Confined Lewis Pairs: Investigation of the X- →Si20 Interaction in Halogen-Encapsulating Silafulleranes

A joint theoretical and experimental study on 32 endohedral silafullerane derivatives [X@Si20 Y20 ]- (X=F-I; Y=F-I, H, Me, Et) andT h ${T_h }$ -[Cl@Si20 H12 Y8 ]- (Y=F-I) is presented. First, we evaluated the structure-determining template effect of Cl- in a systematic series of concave silapolyquinane model systems. Second, we investigated the X- →Si20 interaction energy (E int ${E_{{\rm{int}}} }$ ) as a function of X- and Y and found the largestE int ${E_{{\rm{int}}} }$ values for electron-withdrawing exohedral substituents Y. Given that X- ions can be considered as Lewis bases and empty Si20 Y20 clusters as Lewis acids, we classify our inseparable host-guest complexes [X@Si20 Y20 ]- as "confined Lewis pairs". Third, 35 Cl NMR spectroscopy proved to be highly diagnostic for an experimental assessment of the Cl- →Si20 interaction as the paramagnetic shielding and, in turn, δ ${\delta }$ (35 Cl) of the endohedral Cl- ion correlate inversely withE int ${E_{{\rm{int}}} }$ . Finally, we disclose the synthesis of [PPN][Cl@Si20 Y20 ] (Y=Me, Et, Br) and provide a thorough characterization of these new silafulleranes.

Cl@Si20X20 cages: evaluation of encapsulation nature, structural rigidity, and 29Si-NMR patterns using relativistic DFT calculations

The experimental characterization of Cl@Si₂₀ endohedral clusters, featuring different ligands such as [Cl@Si₂₀H₂₀]^- (1) [Cl@Si₂₀H₁₂Cl₈]^- (2), and [Cl@Si₂₀Cl₂₀]^- (3), provides insight into the variable encapsulation environment for chloride anions. The favorable formation of such species enables the evaluation of the encapsulation nature and the role of the inner anion in the rigidity of the overall cluster. Our results show a sizable interaction which increases as -66.7, -100.8, and -130.3 kcal mol^-1 from 1 to 3, respectively, featuring electrostatic character. The orbital interaction involves 3p-Cl → Si₂₀X₂₀ and 3s-Cl → Si₂₀X₂₀ charge transfer channels and a slight contribution from London dispersion-type interactions. These results show that the inner bonding environment can be modified by the choice of exobonded ligands. Moreover, ²⁹Si-NMR parameters are depicted in terms of the chemical shift anisotropy (CSA), leading to a strong variation of the three principal tensor components (δ₁₁, δ₂₂, δ₃₃), unraveling the origin of the experimental ²⁹Si-NMR chemical shift (δ_iso) differences along the given series. Thus, the Si₂₀ cage is a useful template to further evaluate different environments for encapsulating atomic species.

Study on the growth behavior and photoelectron spectroscopy of neodymium-doped silicon nanoclusters NdSin0/- (n = 8-20) with a double-hybrid density functional theory

Structural evolution, magnetic moment, and thermochemical and spectral properties of NdSi_n^0/- (n = 8-20) nanoclusters were studied. Optimized structures for NdSi_n demonstrated that the configuration with quintet ground state prefers Nd-substituted for a Si of the most stable Si_n + 1 (n = 8-11) structure to Nd-linked configuration with Si₉ tricapped trigonal prism subcluster (n = 12-19). Finally, the configuration prefers to Nd-encapsulated into Si cage framework (n = 20). For anion, the evolution at the quartet state prefers Nd-linked structure for n = 8-19 (excluded 9), and prefers Nd-encapsulated structure of n = 20. The spectral information including electron affinity, vertical detachment energy, and simulated photoelectron spectroscopy were also observed. The 4f electrons of Nd atom in NdSi_n with n = 8-10 hardly participate in bonding, but take part in remaining neutral clusters and all anionic NdSi_n^- clusters. The calculations of average bond energy, HOMO-LUMO gap, and chemical bonding analyses reveal that NdSi₂₀^- possesses perfect thermodynamic and ideal chemical stability, making it as the most appropriate constitutional units for novel multi-functional semiconductors.

Diffusion Monte Carlo Perspective on the Spin-State Energetics of [Fe(NCH)6](2.)

The energy difference between the high spin and the low spin state of the model compound [Fe(NCH)6](2+) is investigated by means of Diffusion Monte Carlo (DMC), where special attention is dedicated to analyzing the effect of the fix node approximation on the accuracy of the results. For this purpose, we compare several Slater-Jastrow and multireference Slater-Jastrow trial wave functions. We found that a Slater-Jastrow trial wave function constructed with the generalized Kohn-Sham orbitals from hybrid DFT represents the optimal choice. This is understood by observing that hybrid functionals account for the subtle balance between exchange and correlation effects and the respective orbitals accurately describe the ligand-metal hybridization as well as the charge reorganization accompanying the spin transition. Finally the DMC results are compared with those obtained by Hartree-Fock, DFT, CASSCF, and CASPT2. While there is no clear reference value for the high spin-low spin energy difference, DMC and high level CCSD(T) calculations agree within around 0.3 eV.

The impact of electron correlations on the energetics and stability of silicon nanoclusters

The first-principles prediction of stable nanocluster structure is often hampered by the existence of many isomer configurations with energies close to the ground state. This fact attaches additional importance to many-electron effects beyond density functional theory (DFT), because their contributions can change a subtle energy order of competitive structures. To analyze this problem, we consider, as an example, the energetics of silicon nanoclusters passivated by hydrogen Si10H2n (0 ≤ n ≤ 11), where passivation changes the structure from compact to loosely packed and branched. Our calculations performed with DFT, hybrid functionals, and Hartree-Fock methods, as well as by the GW approximation, confirm a considerable sensitivity of isomer energy ordering to many-electron effects.

Evaluation of optical and electronic properties of silicon nano-agglomerates embedded in SRO: applying density functional theory

In systems in atomic scale and nanoscale such as clusters or agglomerates constituted by particles from a few to less than 100 atoms, quantum confinement effects are very important. Their optical and electronic properties are often dependent on the size of the systems and the way in which the atoms in these clusters are bonded. Generally, these nanostructures display optical and electronic properties significantly different to those found in corresponding bulk materials. Silicon agglomerates embedded in silicon rich oxide (SRO) films have optical properties, which have been reported to be directly dependent on silicon nanocrystal size. Furthermore, the room temperature photoluminescence (PL) of SRO has repeatedly generated a huge interest due to its possible applications in optoelectronic devices. However, a plausible emission mechanism has not been widely accepted in the scientific community. In this work, we present a short review about the experimental results on silicon nanoclusters in SRO considering different techniques of growth. We focus mainly on their size, Raman spectra, and photoluminescence spectra. With this as background, we employed the density functional theory with a functional B3LYP and a basis set 6-31G* to calculate the optical and electronic properties of clusters of silicon (constituted by 15 to 20 silicon atoms). With the theoretical calculation of the structural and optical properties of silicon clusters, it is possible to evaluate the contribution of silicon agglomerates in the luminescent emission mechanism, experimentally found in thin SRO films.

Computational design of in vivo biomarkers

Fluorescent semiconductor nanocrystals (or quantum dots) are very promising agents for bioimaging applications because their optical properties are superior compared to those of conventional organic dyes. However, not all the properties of these quantum dots suit the stringent criteria of in vivo applications, i.e. their employment in living organisms that might be of importance in therapy and medicine. In our review, we first summarize the properties of an 'ideal' biomarker needed for in vivo applications. Despite recent efforts, no such hand-made fluorescent quantum dot exists that may be considered as 'ideal' in this respect. We propose that ab initio atomistic simulations with predictive power can be used to design 'ideal' in vivo fluorescent semiconductor nanoparticles. We briefly review such ab initio methods that can be applied to calculate the electronic and optical properties of very small nanocrystals, with extra emphasis on density functional theory (DFT) and time-dependent DFT which are the most suitable approaches for the description of these systems. Finally, we present our recent results on this topic where we investigated the applicability of nanodiamonds and silicon carbide nanocrystals for in vivo bioimaging.

The influence of the stacking orientation of C and BN stripes in the structure, energetics, and electronic properties of BC2N nanotubes

Carbon and boron nitride nanotubes present significant differences in their electronics. However, they have isoelectronic bonds and very similar geometrical structures that allow BCN nanotubes to be synthesized. These BCN nanotubes present properties that can vary according to their relative number of B, C, and N atoms, and their atomic distribution on the nanotube surface. Here we employ first-principles density functional theory to study BCN nanotubes with BC(2)N stoichiometry. These nanotubes are composed of pure BN and C stripes which are stacked (i) in parallel, (ii) perpendicularly, and (iii) forming helicoidal patterns along the nanotube axes. We found that the different strain energies of the curved C and BN arcs in the nanotubes with parallelly aligned stripes can lead to geometries that deviate significantly from the usual circular shape. A sinusoidal shape was predicted for a BC(2)N nanotube with a helicoidal arrangement of the C and BN stripes due to differences in the C-B and C-N bonds parallel to the tube axis. It was shown that the phase segregation is energetically favoured. Such structural preference and the relative stability of the BC(2)N nanotubes can be explained in terms of the ratio between the total number of bonds and the number of C-B and C-N bonds in the nanotubes. Finally, we found that one type of BC(2)N nanotube with helicoidal C and BN stripes, although having a zigzag structure, exhibits a metallic character.

An ab initio two-center tight-binding approach to simulations of complex materials properties

We describe theab initioconstruction of two-center tight-binding (TB) hamiltonians, which at a properly chosen input density upon non-selfconsistent solution of the related Kohn-Sham equations transform the energy within density-functional theory (DFT) into a tight-bindinglike expression. In cases, where the electron density of the interacting many-atom structure in good approximation may be represented as a sum of atomic-like densities, the method has been shown to operate highly transferable, being particularly successful in determining the properties of low-energy silicon clusters, in predicting the structure and vibrational signatures of fullerene oligomers, amorphous carbons and carbon nitrides and in simulating elementary growth reactions on diamond surfaces. The uncertainties within the standard non-SCF DF-TB-variant, however, increase if the chemical bonding is controlled by a delicate charge balance between different atomic constituents, as e.g. in organic molecules and in polar semiconductors. Therefore, we extend the standard TB-approach to the operation in a selfconsistent-charge mode(SCC-DFTB)in order to improve total energies, forces, and transferability in the presence of considerable long-range Coulomb interactions. By using a variational technique, we derive a transparent and readily calculable expression for the iterative modification of Hamiltonian matrix elements and show, that the final energy is a second order approximation to the total energy in density-functional theory,see M. Elstner et al., this Symposium.First successful applications to surface studies of GaAs and dislocation modeling in GaN will be presented.

Structures and relative stability of medium-sized silicon clusters. IV. Motif-based low-lying clusters Si21-Si30

Structures and relative stability of four families of low-lying silicon clusters in the size range of Sin(n=21-30) are studied, wherein two families of the clusters show prolate structures while the third one shows near-spherical structures. The prolate clusters in the first family can be assembled by connecting two small-sized magic clusters Sin (n=6, 7, 9, or 10) via a fused-puckered-hexagonal-ring Si9 unit (a fragment of bulk diamond silicon), while those in the second family can be constructed on the basis of a structural motif consisting of a puckered-hexagonal-ring Si6 unit (also a fragment of bulk diamond silicon) and a small-sized magic cluster Sin (n=6, 7, 9, or 10). For Si21-Si29, the predicted lowest-energy clusters (except Si27) exhibit prolate structures. For clusters larger than Si25, the third family of near-spherical clusters becomes energetically competitive. These near-spherical clusters all exhibit endohedral cagedlike structures, and the cages are mostly homologue to the carbon-fullerene cages which consist of pentagons and hexagons exclusively. In addition, for Si26-Si30, we construct a new (fourth) family of low-lying clusters which have "Y-shaped" three-arm structures, where each arm is a small-sized magic cluster (Si6, Si7, or Si10). Density-functional calculation with the B3LYP functional shows that this new family of clusters is also energetically competitive, compared to the two prolate and one near-spherical low-lying families.

Theoretical Study of Mixed Silicon−Lithium Clusters SinLip(+) (n = 1−6, p = 1−2)

Theoretical study on the structures of neutral and singly charged Si(n)Li(p)((+)) (n=1-6, p=1-2) clusters have been carried out in the framework of the density functional theory (DFT) with the B3LYP functional. The structures of the neutral Si(n)Li(p) and cationic Si(n)Li(p)(+) clusters are found to keep the frame of the corresponding Si(n), Li species being adsorbed at the surface. The localization of the lithium cation is not the same one as that of the neutral atom. The Li(+) ion is preferentially located on a Si atom, while the Li atom is preferentially attached at a bridge site. A clear parallelism between the structures of Si(n)Na(p) and those of Si(n)Li(p) appears. The population analysis show that the electronic structure of Si(n)Li(p) can be described as Si(n)(p)(-)+pLi(+) for the small sizes considered. Vertical and adiabatic ionization potentials, adsorption energies, as well as electric dipole moments and static dipolar polarizabilities, are calculated for each considered isomer of neutral species.

Quantum Monte Carlo method using a stochastic Poisson solver

The quantum Monte Carlo (QMC) technique is an extremely powerful method to treat many-body systems. Usually the quantum Monte Carlo method has been applied in cases where the interaction potential has a simple analytic form, like the 1/r Coulomb potential. However, in a complicated environment as in a semiconductor heterostructure, the evaluation of the interaction itself becomes a nontrivial problem. Obtaining the potential from any grid-based finite-difference method for every walker and every step is infeasible. We demonstrate an alternative approach of solving the Poisson equation by a classical Monte Carlo calculation within the overall quantum Monte Carlo scheme. We have developed a modified "walk on spheres" algorithm using Green's function techniques, which can efficiently account for the interaction energy of walker configurations, typical of quantum Monte Carlo algorithms. This stochastically obtained potential can be easily incorporated with variational, diffusion, and other Monte Carlo techniques. We demonstrate the validity of this method by studying a simple problem, the polarization of a helium atom in the electric field of an infinite capacitor.

An investigation of nodal structures and the construction of trial wave functions

The factors influencing the quality of the nodal surfaces, namely, the atomic basis set, the single-particle orbitals, and the configurations included in the wave-function expansion, are examined for a few atomic and molecular systems. The following empirical rules are found: the atomic basis set must be fairly large, complete active space and natural orbitals are usually better than Hartree-Fock orbitals, multiconfiguration expansions perform better than single-determinant wave functions, but only few configurations are effective and their choice is suggested by symmetry considerations, while too long determinantal expansions spoil the nodal surfaces. These rules allow us to reduce the nodal error and to compute the best fixed node-diffusion Monte Carlo energies for a series of dimers of first-row atoms.

Structure, Strain, and Degenerate Rearrangement of Tricyclo[2.1.0.0]pentasilane and Related Molecules

We theoretically investigate a highly strained tricyclic silane (tricyclo[2.1.0.0 1,3]pentasilane (4b), an isomer of pentasila[1.1.1]propellane (3b)) composed of three fused three-membered rings. The central ring is distorted. One of the fusion bonds in the central ring is shorter than the normal Si-Si single bond (2.350 A) whereas the other is as long as the fusion bonds in bicyclo[1.1.0]tetrasilane (2b) (2.860 A) and 3b (2.778 A). The tricyclic silane is less strained than the carbon congener and more strained than the isomer 3b. The electron delocalization between one of the fusion bonds and the geminal Si-Si ring bonds elongates the fusion bond and stabilizes the molecules to reduce the strain. The silanes composed of the fused three-membered rings are less strained than the carbon congener. A degenerate rearrangement of a three-membered ring is predicted. The enthalpy of activation of the rearrangement of the distorted central ring is low (7.2 kcal/mol) for 4b, but appreciable (22.3 kcal/mol) for the germanium congener, tricyclo[2.1.0.0(1,3)]pentagermane (4c). We investigate the effects of the substituents on the distortion of the central three-membered ring and the degenerate rearrangement.

Multiple Aromaticity and Antiaromaticity in Silicon Clusters

A series of silicon clusters containing four atoms but with different charge states (Si4(2+), Si4, Si4(2-), and NaSi4-) were studied by photoelectron spectroscopy and ab initio calculations. Structure evolution and chemical bonding in this series were interpreted in terms of aromaticity and antiaromaticity, which allowed the prediction of how structures of the four-atom silicon clusters change upon addition or removal of two electrons. It is shown that Si4(2+) is square-planar, analogous to the recently discovered aromatic Al4(2-) cluster. Upon of two electrons, neutral Si4 becomes sigma-antiaromatic and exhibits a rhombus distortion. Adding two more electrons to Si4 leads to two energetically close structures of Si4(2-): either a double antiaromatic parallelogram structure or an aromatic system with a butterfly distortion. Because of the electronic instability of doubly charged Si4(2-), a stabilizing cation (Na+) was used to produce Si4(2-) in the gas phase in the form of Na+[Si4(2-)], which was characterized experimentally by photoelectron spectroscopy. Multiple antiaromaticity in the parallelogram Na+[Si4(2-)] species is highly unusual.

Structures and stability of medium silicon clusters. II. Ab initio molecular orbital calculations of Si12–Si20

Ab initio all-electron molecular-orbital calculations are carried out to study the structures and relative stability of low-energy silicon clusters (Si(n),n = 12-20). Selected geometric isomers include those predicted by Ho et al. [Nature (London) 392, 582 (1998)] based on an unbiased search with tight-binding/genetic algorithm, as well as those found by Rata et al. [Phys. Rev. Lett. 85, 546 (2000)] based on density-functional tight-binding/single-parent evolution algorithm. These geometric isomers are optimized at the Møller-Plesset (MP2) MP2/6-31G(d) level. The single-point energy at the coupled-cluster single and double substitutions (including triple excitations) [CCSD(T)] CCSD(T)/6-31G(d) level for several low-lying isomers are further computed. Harmonic vibrational frequency analysis at the MP2/6-31G(d) level of theory is also undertaken to assure that the optimized geometries are stable. For Si12-Si17 and Si19 the isomer with the lowest-energy at the CCSD(T)/6-31G(d) level is the same as that predicted by Ho et al., whereas for Si18 and Si20, the same as predicted by Rata et al. However, for Si14 and Si15, the vibrational frequency analysis indicates that the isomer with the lowest CCSD(T)/6-31G(d) single-point energy gives rise to imaginary frequencies. Small structural perturbation onto the Si14 and Si15 isomers can remove the imaginary frequencies and results in new isomers with slightly lower MP2/6-31G(d) energy; however the new isomers have a higher single-point energy at the CCSD(T)/6-31G(d) level. For most Si(n) (n = 12-18,20) the low-lying isomers are prolate in shape, whereas for Si19 a spherical-like isomer is slightly lower in energy at the CCSD(T)/6-31G(d) level than low-lying prolate isomers.

Investigating bonding in small silicon–carbon clusters: Exploration of the potential energy surfaces of Si3C4, Si4C3, and Si4C4 using ab initio molecular dynamics

A theoretical investigation of the properties of the Si3C4, Si4C3, and Si4C4 clusters is reported. Systematic explorations of the potential energy surfaces of the three clusters are performed using a combination of ab initio molecular dynamics and local energy minimizations using density functional theory. A large number of isomers with a large variety of geometries has been found. The geometries, energies, and vibrational frequencies yielded are discussed. Furthermore, a quantitative analysis of the interatomic distances, angles, and coordination numbers observed, as well as the conclusions on the bonding properties, are presented. The cluster properties are then compared to those of solid SiC and of the smaller Si-C clusters (with size up to 6) obtained in a previous study. Analysis of our results and comparison with bulk properties show that even clusters as small as Si3C4, Si4C3, and Si4C4 exhibit properties similar to those of the amorphous bulk, in particular as for the structures and bonds formed by C atoms.

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.