Emerging polymorphism in nanostructured TiO2: Quantum chemical comparison of anatase,rutile, and brookite clusters

Density functional theory (DFT) and time‐dependent DFT calculations have been performed on a set of 34 titanium dioxide clusters ((TiO2)_n with n ≤ 125) to investigate structural and electronic properties of nanostructured TiO₂ (nano‐TiO₂) materials. The investigated clusters include models of the three low‐energy polymorphic forms of TiO₂ anatase, rutile, and brookite. A systematic comparison of clusters of increasing size show clear trends for emerging bulk properties in the investigated systems as the surface‐to‐bulk ratio changes from small clusters dominated by undercoordinated surface atoms to more realistic model nanocrystals with significant bulk components. Differences and similarities in terms of atomic coordination, structural stability, and electronic properties for the three different polymorphic forms of nano‐TiO₂ are discussed. The calculations provide evidence for emerging polymorphism with increasing cluster sizes so that the different TiO₂ forms can be clearly distinguished based on structural characteristics associated with the local bonding environment of the constituent atoms. © 2013 Wiley Periodicals, Inc.     

Density functional finite cluster method for polarizability of large BeN three‐dimensional systems

The structures and the properties of small clusters are known to be quite different from those of the bulk material. Consequently, the focus of most studies is towards understanding the changes in electronic properties with increasing cluster size. Linear static electronic dipole polarizabilities of the Be_N (N→∞) solid are obtained at the DFT(PWB91) level by extrapolation of ab initio calculations on Be_N (N=1,…,132) clusters. For the mean polarizability, a [5s3p] basis set is shown to give accurate values if the tri‐periodic clusters are big enough. No calculation has yet been carried out on Be_N (N→∞), but it is clear that these linear properties converge relatively slowly with cluster size. For Be_N, cluster size up to N=90 atoms are sufficient to give limiting infinite solid polarizabilities with relatively small uncertainties. For N=132, the mean polarizability result is probably very accurate. These results suggest that DFT is a good method for the determination of these properties. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 230–240, 2001     

Insights into the dynamics of evaporation and proton migration in protonated water clusters from Large‐scale Born–Oppenheimer direct dynamics

Large‐scale on‐the‐fly Born–Oppenheimer molecular dynamics simulations using recent advances in linear scaling electronic structure theory and trajectory integration techniques have been performed for protonated water clusters around the magic number (H₂O)_nH⁺, for n = 20 and 21. Besides demonstrating the feasibility and efficiency of the computational approach, the calculations reveal interesting dynamical details. Elimination of water molecules is found to be fast for both cluster sizes but rather insensitive to the initial geometry. The water molecules released acquire velocities compatible with thermal energies. The proton solvation shell changes between the well‐known Eigen and Zundel motifs and is characterized by specific low‐frequency vibrational modes, which have been quantified. The proton transfer mechanism largely resembles that of bulk water but one interesting variation was observed. © 2012 Wiley Periodicals, Inc.     

Solvent effect on the tautomers' stabilities of protonated N,N‐dimethylnitrosamine: The role of hydrogen bonds network

DFT calculations have been applied in order to study the free energies of the structures corresponding to the three different protonation sites of N,N‐dimethylnitrosamine (DMNA). The solvent effect has been taken into account through the study of clusters consisting of protonated DMNA and up to four explicit water molecules, either in the absence or in the presence of a continuum (CPCM) solvation model. Addition of water molecules has been done by a careful screening procedure through which all important hydrogen bonds are likely to be considered. Protonation of DMNA makes all their lone pairs no longer available for hydrogen bond formation with water molecules, such that hydrogen bonds have been observed, for almost all structures, only between water molecules and between one water molecule and the protonated DMNA, in this latter case intermediated by the proton. The stabilities of the solvated structures are governed not only by the number of hydrogen bonds but also by the positions of the water molecules involved in these bonds, as well as by which of them donate or accept H atoms. Our results indicate that oxygen protonation is the most favorable one, regardless of the presence of water molecules. In vacuum protonation at the N‐amino ( 2a ) is approximately as favorable as protonation at the N nitroso ( 2c ). However, in water the former protonation is by far the less favorable one. Our best estimates for the ΔG values in bulk solvent are: ΔG( 2a ) ≈ 17.9, ΔG( 1c ) ≈ 4.3, and ΔG( 2c ) ≈ 4.9 kcal/mol.     

Conformational and electronic study of N‐acetyl‐L‐isoleucine‐N‐methylamide using DFT and IPCM calculations

A conformational and electronic study on N‐acetyl‐L ‐isoleucine‐N‐methylamide was carried out. All side‐chain as well as backbone conformations were explored for this compound. Multidimensional conformational analysis predicts 81 structures in the case of N‐acetyl‐L ‐isoleucine‐N‐methylamide, 53 relaxed structures were determined at the DFT (B3LYP/6‐31G(d)) level of theory. An exhaustive electronic study employing the atoms‐in‐molecules (AIM) method was carried out. In addition, the effects of three solvents (water, acetonitrile, and chloroform) were included in the calculations using the isodensity polarizable continuum model (IPCM) method. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Silicon clusters: chemistry and structure

The chemical reactions of size selected silicon cluster ions (containing up to 70 atoms) have been studied with a number of different reagents using injected ion drift tube techniques. Both kinetic and equilibrium measurements have been performed as a function of temperature, and the influence of cluster annealing on chemical reactivity explored. Unlike metal clusters, where bulk behavior appears to be approached with around 30 atoms, large silicon clusters (n up to 70) are much less reactive than bulk silicon surfaces. These results suggest that the clusters in the size range examined here are not small crystals of bulk silicon, but have compact, high coordination number structures with few dangling bonds.     

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     

Theoretical study of silicon–sulfur clusters (SiS2)n− (n=1–6)

The possible geometrical structures and relative stability of silicon–sulfur clusters (SiS₂) (n=1–6) are explored by means of density functional theory (DFT) quantum chemical calculations. We also compare DFT with second‐order Møller–Plesset (MP2) and Hartree–Fock (HF) methods. The effects of polarization functions, diffuse functions, and electron correlation are included in MP2 and B3LYP quantum chemical calculations, and B3LYP is effective in larger cluster structure optimization, so we can conclude that the DFT approach is useful in establishing trends. The electronic structures and vibrational spectra of the most stable geometrical structures of (SiS₂)_n⁻ are analyzed by B3LYP. As a result, the regularity of the (SiS₂)_n⁻ cluster growing is obtained, and the calculation may predict the formation mechanism of the (SiS₂)_n⁻ cluster. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 280–290, 2001     

N‐Arylation of Diketopyrrolopyrroles with Aryl Triflates

A new methodology for the double N‐arylation of diketopyrrolopyrroles with aryl triflates has been developed. It is now possible to prepare diketopyrrolopyrroles bearing N‐substituents derived from naphthalene, anthracene and coumarin in two steps from commercially available phenols. This represents the first time arenes lacking strong electron‐withdrawing groups were inserted onto lactamic nitrogen atoms via arylation. The ability to incorporate heretofore unprecedented substituents translates to increased modulation of the resulting photophysical properties such as switching‐on/off solvatofluorochromism. TD‐DFT calculations have been performed to explore the nature of the relevant excited states. This new synthetic method made it possible to elucidate the influence of such substituents on the absorption and emission properties of tetraaryl substituted diketopyrrolopyrroles.     

An ab initio study of water clusters in gas phase and bulk aqueous media: (H2O)n,n=1–12

Geometries of several clusters of water molecules including single minimum energy structures of n‐mers (n=1–5), several hexamers and two structures of each of heptamer to decamer derived from hexamer cage and hexamer prism were optimized. One structural form of each of 11‐mer and 12‐mer were also studied. The geometry optimization calculations were performed at the RHF/6‐311G* level for all the cases and at the MP2/6‐311++G** level for some selected cases. The optimized cluster geometries were used to calculate total energies of the clusters in gas phase employing the B3LYP density functional method and the 6‐311G* basis set. Frequency analysis was carried out in all the cases to ensure that the optimized geometries corresponded to total energy minima. Zero‐point and thermal free energy corrections were applied for comparison of energies of certain hexamers. The optimized cluster geometries were used to solvate the clusters in bulk water using the polarized continuum model (PCM) of the self‐consistent reaction field (SCRF) theory, the 6‐311G* basis set, and the B3LYP density functional method. For the cases for which MP2/6‐311++G** geometry optimization was performed, solvation calculations in water were also carried out using the B3LYP density functional method, the 6‐311++G** basis set, and the PCM model of SCRF theory, besides the corresponding gas‐phase calculations. It is found that the cage form of water hexamer cluster is most stable in gas phase among the different hexamers, which is in agreement with the earlier theoretical and experimental results. Further, use of a newly defined relative population index (RPI) in terms of successive total energy differences per water molecule for different cluster sizes suggests that stabilities of trimers, hexamers, and nonamers in gas phase and those of hexamers and nonamers in bulk water would be favored while those of pentamer and decamer in both the phases would be relatively disfavored. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 90–104, 2001     

Synthesis,spectroscopy, X-ray crystal structure,and DFT studies on a platinum(II) Schiff-base complex

[PtCl₂(SMe₂)₂] reacts with (N,N′-bis(salicylidene)-1,2-cyclohexanediamine) to give (N,N′-bis(salicylidene)cyclohexane-1,2-diamine)platinum(II). The complex has been characterized by elemental analysis, infrared (IR), UV-Vis, and single-crystal X-ray diffraction. Pt(II) is in a square-planar environment, coordinated by a chelating N₂O₂ donor. Density functional theory (DFT) calculations such as geometry optimization, vibrational frequency, electronic properties, and natural bond orbital (NBO) have been performed for the platinum compound using the OLYP method at TZP(6-311G*) basis set. The optimization calculation shows that the geometry parameters can be reproduced with the OLYP/TZP basis set. Experimental IR frequencies and calculated vibrational frequencies support each other. Time-dependent DFT has been used for absorption wavelengths and results were compared with experimental data. Moreover, NBO analysis has been performed.     

A Novel High-Pressure Tin Oxynitride Sn2N2O

We report the first oxynitride of tin, Sn₂N₂O (SNO), exhibiting a Rh₂S₃-type crystal structure with space group Pbcn. All Sn atoms are in six-fold coordination, in contrast to Si in silicon oxynitride (Si₂N₂O) and Ge in the isostructural germanium oxynitride (Ge₂N₂O), which appear in four-fold coordination. SNO was synthesized at 20 GPa and 1200–1500 °C in a large volume press. The recovered samples were characterized by synchrotron powder X-ray diffraction and single-crystal electron diffraction in the TEM using the automated diffraction tomography (ADT) technique. The isothermal bulk modulus was determined as B_o=193(5) GPa by using in-situ synchrotron X-ray diffraction in a diamond anvil cell. The structure model is supported by DFT calculations. The enthalpy of formation, the bulk modulus, and the band structure have been calculated.     

Investigation of the Second Harmonic Generation at the Water–Vacuum Interface by Using Multi-Scale Modeling Methods

The Sequential Quantum Mechanics/Molecular Mechanics scheme has been enacted to perform a systematic investigation of the polarizability (α) and first hyperpolarizability (β) responses at the water–vacuum interface. After performing classical molecular dynamics simulations to provide snapshots of the structures, quantum chemistry calculations of the linear and nonlinear optical responses have been performed for clusters of five water molecules at the time-dependent DFT level in combination with different embedding schemes, ranging from point charges to polarizable point charges, with and without local field effects. When going from the bulk to the interface, the main observations of these calculations encompass i) a modest increase of the average polarizability but an increase by about a factor of two of its anisotropy, ii) an increase by about 20 % of the β_HRS response, accompanied by a small increase of its depolarization ratio, and iii) a net increase of the component of the β tensor normal to the interface (β_zzz) as well as of β_//. Globally, the interfacial effects on β are localized at the first molecular layer while they are observed up to the fourth molecular layer on α.     

B<Subscript>24</Subscript>N<Subscript>24</Subscript> nanocages: a GIAO density functional theory study of <Superscript>14</Superscript>N and <Superscript>11</Superscript>B nuclear magnetic shielding and electric field gradient tensors

Abstract  Density functional theory (DFT) calculations were performed to determine boron-11 and nitrogen-14 nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) spectroscopy parameters in the three most stable B₂₄N₂₄ fullerenes for the first time. The considered samples were first allowed to relax entirely, and then the NMR and NQR calculations were performed on the geometrically optimized models. The calculations of the ¹¹B and ¹⁴N nuclear magnetic shielding tensors and electric field gradient tensors employed the Gaussian 98 software implementation of the gauge-including atomic orbital (GIAO) method using the Becke3, Lee-Yang-Parr (B3LYP) DFT level and 6-311G** and 6-311++G** standard basis sets in each of the three optimized forms, and converted the results to experimentally measurable NMR parameters.The calculated NMR chemical shieldings of the three cages show significant differences, providing a way to identify these clusters. The evaluated NQR parameters of the ¹¹B and ¹⁴N nuclei in the clusters are also reported and discussed. Graphical abstract        

A DFT Study on the Conversion of Aryl Iodides to Alkyl Iodides: Reductive Elimination of R−I from Alkylpalladium Iodide Complexes with Accessible β‐Hydrogens

DFT calculations have been performed on the palladium‐catalyzed carboiodination reaction. The reaction involves oxidative addition, alkyne insertion, C?N bond cleavage, and reductive elimination. For the alkylpalladium iodide intermediate, LiOtBu stabilizes the intermediate in non‐polar solvents, thus promoting reductive elimination and preventing β‐hydride elimination. The C?N bond cleavage process was explored and the computations show that PPh₃ is not bound to the Pd center during this step. Experimentally, it was demonstrated that LiOtBu is not necessary for the oxidative addition, alkyne insertion, or C?N bond cleavage steps, lending support to the conclusions from the DFT calculations. The turnover‐limiting steps were found to be C?N bond cleavage and reductive elimination, whereas oxidative addition, alkyne insertion, and formation of the indole ring provide the driving force for the reaction.     

A fragment multipole approach to long-range Coulomb interactions in Hartree–Fock calculations on large systems

An efficient ab initio method for electronic structure calculations on extended molecular systems is presented, along with some illustrative applications. A division of the system into subunits allows the interactions to be separated into short- and long-range contributions, leading to a reduction of the computational effort from the original fourth-power size-dependence to one that is approximately quadratic. The short-range contributions to the Fock matrix are obtained in an essentially conventional fashion, while the long-range interactions are evaluated using a two-center multipole expansion formalism. The number of short-range contributions grows only linearly with the number of subunits, while the long-range contributions grow as N². Systematic studies of the computational efforts for systems of up to 99 water molecules organized as one-stranded chains, three-stranded chains, and three-dimensional clusters, as well as alkane chains with up to 69 carbon atoms, have been performed. In these model systems, the overall computational effort grows as N^K where 1 < K < 2.     

Influence of nitroxide structure on polystyrene brushes “grafted‐from” silicon wafers

Alkoxyamine derivatives based on 2,2,6,6‐tetramethyl‐1‐piperidinyloxy (TEMPO), N‐tert‐butyl‐N‐(1‐diethylphosphono‐(2,2‐dimethylpropyl)) nitroxide (SG1) and N‐tert‐butyl‐N‐(2‐methyl‐1‐phenylpropyl) nitroxide (TIPNO) containing a C₁₁ hydrophobic spacer and a reactive triethoxysilyl polar head, were synthesized and anchored to silicon wafers by the Langmuir–Blodgett reactive deposition technique at surface pressures ranging from 15 to 32 mN/m. Polystyrene brushes (M_n ～ 8500–66,400 g/mol) were grown from the alkoxyamine functionalized silicon wafers by nitroxide mediated radical polymerization and characterized by ellipsometry and water contact angle measurements. The main parameters influencing the grafting density and the degree of stretching of the brushes are the nitroxide polarity and, therefore, the behavior of the corresponding alkoxyamines at the air/water interface of the Langmuir–Blodgett trough. Depending on the alkoxyamine chemical structure and the surface pressure during Langmuir–Blodgett deposition, polystyrene brushes with grafting densities of 0.3–1.0 chains/nm² and stretching values of 40–70% were obtained. Regarding alkoxyamines deposited at high surface pressures, size exclusion chromatography experiments performed on both cleaved polystyrene brushes and chains simultaneously grown in the bulk revealed that the polymerization degree of the bulk and surface chains are significantly different, suggesting that steric constrains affect the polymerization kinetics occurring at the silicon surface. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3367–3374, 2008     

Density functional studies on hydrogen‐bonded clusters of hydrogen halides and the interaction on halide anions

Density functional theory (DFT) calculations have been performed to study the structures and stability of X^?·(HX)_n=2–5 clusters where X = F, Cl, Br at B3LYP/6‐311++G** level of theory. The presence of halide ions in these clusters disintegrates the hydrogen halide clusters. All the hydrogen halides are then hydrogen bonded to the centrally placed halide ions, thereby forming multiple hydrogen bonds. The interaction energies have been corrected for the basis set superposition error (BSSE) using Boy's counterpoise correction method. Evidence for the destruction of hydrogen bonds in hydrogen halide clusters due to the presence of halide ions is further obtained from topological analysis and natural bond orbital analysis. The chemical hardness and chemical potential have been calculated for all the anion clusters. The above analysis reveals that hydrogen bonding in these systems is not an essentially electrostatic interaction. The nature of the stabilization interactions operative in these multiple hydrogen‐bonded clusters has been explained in terms of many‐body contribution to interaction energies. From these studies, an attempt has been made to understand the nature of the molecular properties resulting from different electronegativities of the halogens. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Observable Structures of Small Neutral and Anionic Gold Clusters

Since gold clusters have mostly been studied theoretically by using DFT calculations, more accurate studies are of importance. Thus, small neutral and anionic gold clusters (Au_n and Au_n^?, n=4–7) were investigated by means of coupled cluster with singles, doubles, and perturbative triple excitations [CCSD(T)] calculations with large basis sets, and some differences between DFT and CCSD(T) results are discussed. Interesting isomeric structures that have dangling atoms were obtained. Structures having dangling atoms appear to be stable up to n=4 for neutral gold clusters and up to n=7 for anionic clusters. The relative stabilities and electronic properties of some isomers and major structures are discussed on the basis of the CCSD(T) calculations. This accurate structure prediction of small gold clusters corresponding to experimental photoelectron spectral peaks is valuable in the field of atom‐scale materials science including nanocatalysts.     

Mixed silicon–germanium nanocrystals: a detailed study of Si<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Ge<Subscript>47−<Emphasis Type="Italic">x</Emphasis></Subscript>:H

Mixed SiGe:H nanocrystals have been studied within the framework of Density Functional Theory. (DFT) using the hybrid non-local exchange-correlation functional of Becke, Lee, Parr and Yang (B3LYP). In addition to ground-state DFT/B3LYP calculations, excited-state calculations for the determination of the optical absorption spectrum have been performed employing the time-dependent density functional theory (TDDFT). In order to fully investigate the substitution of Si by Ge, on structural, cohesive, electronic and optical properties, we have used the Si _x Ge_47−x :H nanocrystal, as a representative medium size nanosystem. Our results show that the optical gap depends not only on the relative concentrations of silicon, germanium and hydrogen, but also on the relative position of the silicon and germanium shells relative to the surface of the nanocrystal. This is also true for the structural, cohesive and electronic properties. This dependence allows for the possibility of electronic and optical gap engineering.