Computational studies of stable hexanuclear CulAgmAun (l + m + n = 6; l,m, n > 0) clusters

A DFT study was carried out on the ground state structures of ternary Cu_lAg_mAu_n (l + m + n = 6) clusters, with the aim of investigating changes of thermal and kinetic stabilities as an effect of composition, as well as the composition dependence of the electrostatic potential, of stable planar structures. DFT optimizations were performed using the PBE functional and the SDD basis set. All the optimized structures adopt planar geometries with bent triangular structures. Calculated binding energy values are in the range 1.5–1.9 eV/atom, which shows their thermal stability. The predicted HOMO‐LUMO energy gap values are in the semiconductor region, providing a qualitative indication of a moderate kinetic stability. NBO analyses indicate the existence of two mechanisms promoting planar structural stability, one due to bonding‐antibonding orbital interaction, and the other one due to the well‐known spd hybridization. Wiberg indices were obtained showing interatomic bonding. Electrostatic potential calculations show the existence of nucleophilic attack regions preferentially around silver and copper atoms located at the vertices while electrophilic attack regions are found in the vicinity of gold atoms over the cluster plane. Apparently, charge transfer occurs toward gold from silver and copper atoms when the concentration is favorable in the proximity of gold atoms. In particular, if the small ternary clusters discussed here contain only one gold atom, then a high electron density is observed at the site of this gold atom. © 2016 Wiley Periodicals, Inc.     

六核钽铑二元混合簇合物的几何和电子结构

采用密度泛函理论对六核钽、铑八面体纯簇及其混合簇的几何结构和电子性质进行了研究.计算结果表明:大部分钽铑混合簇稳定构型的对称性均较低,为C1或Cs点群,只有[Ta2Rh4Cl4H8(CN)6]4-团簇的稳定构型对称性较高,为C2h或C4v点群;混合簇的最高占据分子轨道(HOMO)与最低未占据分子轨道(LUMO)能隙(ΔEH-L)均较小,介于0.52-1.00eV之间;混合簇的前线轨道主要由骨架金属原子的d电子贡献,随着Rh原子替代Ta原子个数的递增,Ta—Rh键对混合簇稳定构型所起作用逐渐增加,Ta—Ta键所起作用减小,而Rh—Rh键为非键或反键性质.     

Computational insight into the static and dynamic polarizabilities of aluminum nanoclusters

The static and dynamic polarizabilities for the lowest-energy structures of pure aluminum clusters up to 31 atoms have been investigated systematically within the framework of density functional theory. The size evolution of several electronic properties such as ionization potential, electron affinity, the energy gap between the highest occupied molecular orbital and lowest unoccupied molecular orbital, and chemical hardness have also been discussed for aluminum clusters. Our primary focus in this article, however, has been upon the study of polarizability of aluminum clusters, although we also looked at the role of other electronic properties. From the energetics point of view, the relative stability of aluminum clusters at different sizes is studied in terms of the calculated second-order difference in the total energy of cluster and fragmentation energy, exhibiting that the magic numbers of stabilities are n = 7, 13, and 20. Moreover, the minimum polarizability principle is used to characterize the stability of aluminum clusters. The results show that polarizabilities and electronic properties can reflect obviously the stability of clusters. Electronically, the size dependence of ionization potential and electron affinity of clusters is determined. On the basis of the Wood and Perdew model these quantities converge asymptotically to the value of the bulk aluminum work function.     

Electronic structure and molecular orbital study of the first excited state of the high‐efficiency blue OLED material bis(2‐methyl‐8‐quinolinolato)aluminum(III) hydroxide complex from ab initio and TD‐B3LYP

Bis(2‐methyl‐8‐quinolinolato)aluminum(III) hydroxide complex (AlMq₂OH) is used in organic light‐emitting diodes (OLEDs) as an electron transport material and emitting layer. By means of ab initio Hartree–Fock (HF) and density functional theory (DFT) B3LYP methods, the structure of AlMq₂OH was optimized. The frontier molecular orbital characteristics and energy levels of AlMq₂OH have been analyzed systematically to study the electronic transition mechanism in AlMq₂OH. For comparison and calibration, bis(8‐quinolinolato)aluminum(III) hydroxide complex (Alq₂OH) has also been examined with these methods using the same basis sets. The lowest singlet excited state (S₁) of AlMq₂OH has been studied by the singles configuration interaction (CIS) method and time‐dependent DFT (TD‐DFT) using a hybrid functional, B3‐LYP, and the 6‐31G* basis set. The lowest singlet electronic transition (S₀ → S₁) of AlMq₂OH is π → π* electronic transitions and primarily localized on the different quinolate ligands. The emission of AlMq₂OH is due to the electron transitions from a phenoxide donor to a pyridyl acceptor from another quinolate ligand including C → C and O → N transference. Two possible electron transfer pathways are presented, one by carbon, oxygen, and nitrogen atoms and the other via metal cation Al³⁺. The comparison between the CIS‐optimized excited‐state structure with the HF ground‐state structure indicates that the geometric shift is mainly confined to the one quinolate and these changes can be easily understood in terms of the nodal patterns of the highest occupied and lowest unoccupied molecular orbitals. On the basis of the CIS‐optimized structure of the excited state, TD‐B3‐LYP calculations predict an emission wavelength of 499.78 nm. An absorption wavelength at 380.79 nm on the optimized structure of B3LYP/6‐31G* was predicted. They are comparable to AlMq2OH 485 and 390 nm observed experimentally for photoluminescence and UV‐vis absorption spectra of AlMq₂OH solid thin film on quartz, respectively. Lending theoretical corroboration to recent experimental observations and supposition, the reasons for the blue‐shift of AlMq2OH were revealed. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Fe_(6-x)Al_x团簇的结构和磁性能

在密度泛函理论的BPW91水平上,对Fe6-xAlx团簇进行了结构优化,并将获得的最低能结构进行稳定性分析以及电子结构和磁性能的计算.计算结果表明,铁原子倾向团聚在一起并占据最高配位,Al原子则倾向分布在铁簇的周围尽最大可能地与Fe配位成键.Fe6-xAlx团簇的磁性随Al原子数目增加呈现下降趋势,自然轨道分析揭示Fe4s和Al3s与Fe3d之间的杂化是导致团簇磁矩下降的主要原因.     

Structures and electronic properties of the small rubidium‐doped silicon RbSin (n = 1–12) clusters

The geometries, relative stabilities, and electronic properties of small rubidium‐doped silicon clusters RbSi_n (n = 1–12) have been systematically investigated using the density functional theory at the B3LYP/GENECP level. The optimized structures show that lowest‐energy isomers of RbSi_n are similar with the ground state isomers of pure Si_n clusters and prefer the three‐dimensional for n = 3–12. The relative stabilities of RbSi_n clusters have been analyzed on the averaged binding energy, fragmentation energy, second‐order energy difference, and highest occupied molecular orbital‐lowest unoccupied molecular orbital energy gap. The calculated results indicate that the doping of Rb atom enhances the chemical activity of Si_n frame and the magic number is RbSi₂. The Mulliken population analysis reveals that the charges in the corresponding RbSi_n clusters transfer from the Rb atom to Si atoms. The partial density of states and chemical hardness are also discussed. © 2014 Wiley Periodicals, Inc.     

Structure and energetic of Bn (n = 2–12) clusters: Electronic structure calculations

The electronic and geometric structures, total and binding energies, first and second energy differences, harmonic frequencies, point symmetries, and highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps of small and neutral B_n (n = 2–12) clusters have been investigated using density functional theory (DFT), B3LYP with 6‐311++G(d,p) basis set. Linear, planar, convex, quasi‐planar, three‐dimensional (3D) cage, and open‐cage structures have been found. None of the lowest energy structures and their isomers has an inner atom; i.e., all the atoms are positioned at the surface. Within this size range, the planar and quasi‐planar (convex) structures have the lowest energies. The first and the second energy differences are used to obtain the most stable sizes. A simple growth path is also discussed with the studied sizes and isomers. The results have been compared with previously available theoretical and experimental works. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Density functional study of structural and electronic properties of AlnN (1 ≤ n ≤ 12) clusters

Low‐lying equilibrium geometric structures of Al_nN (n = 1–12) clusters obtained by an all‐electron linear combination of atomic orbital approach, within spin‐polarized density functional theory, are reported. The binding energy, dissociation energy, and stability of these clusters are studied within the local spin density approximation (LSDA) and the three‐parameter hybrid generalized gradient approximation (GGA) due to Becke–Lee–Yang–Parr (B3LYP). Ionization potentials, electron affinities, hardness, and static dipole polarizabilities are calculated for the ground‐state structures within the GGA. It is observed that symmetric structures with the nitrogen atom occupying the internal position are lowest‐energy geometries. Generalized gradient approximation extends bond lengths as compared with the LSDA lengths. The odd–even oscillations in the dissociation energy, the second differences in energy, the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps, the ionization potential, the electron affinity, and the hardness are more pronounced within the GGA. The stability analysis based on the energies clearly shows the Al₇N cluster to be endowed with special stability. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Structural,spectroscopic aspects,and electronic properties of (TiO2)n clusters: A study based on the use of natural algorithms in association with quantum chemical methods

In this article, we propose a stochastic search‐based method, namely genetic algorithm (GA) and simulated annealing (SA) in conjunction with density functional theory (DFT) to evaluate global and local minimum structures of (TiO₂)_n clusters with n = 1–12. Once the structures are established, we evaluate the infrared spectroscopic modes, cluster formation energy, vertical excitation energy, vertical ionization potential, vertical electron affinity, highest occupied molecular orbital (HOMO)‐lowest unoccupied molecular orbital (LUMO) gaps, and so forth. We show that an initial determination of structure using stochastic techniques (GA/SA), also popularly known as natural algorithms as their working principle mimics certain natural processes, and following it up with density functional calculations lead to high‐quality structures for these systems. We have shown that the clusters tend to form three‐dimensional networks. We compare our results with the available experimental and theoretical results. The results obtained from SA/GA‐DFT technique agree well with available theoretical and experimental data of literature. © 2013 Wiley Periodicals, Inc.     

The generation of ground-state structures and electronic properties of ternary AlkTilNim clusters (k + l + m = 4) from a two-stage density functional theory global searching approach

Structural and electronic properties of ternary clusters Al_kTi_lNi_m, where k, l, and m are integers and k + l + m = 4 , are investigated. These clusters are generated and studied by performing a two-stage density functional theory (DFT) calculations using the Slater, Vosko, Wilks, and Nusair (SVWN) and Becke three-parameter, Lee-Yang-Parr (B3LYP) functional exchange correlations. In the first stage, an unbiased global search algorithm coupled with a DFT code with a light exchange-correlation and smaller basis sets are used to generate the lowest energy cluster structures. It is then followed by further optimization using another round of DFT calculation with heavy exchanged correlations and large basis set. Electronic properties of the structures obtained via the two-stage procedure are then studied via DFT calculations. The results are illustrated in the form of ternary diagram. Our DFT calculations find that the stability of the cluster increases with the increase in the number of nickel atoms inside the clusters. Our findings provide new insight into the ternary metallic cluster through the structure, stability, chemical order, and electronic properties studies.     

Photo‐physical Properties of N‐methyl‐3,4‐fulleropyrrolidine and Its Derivatives: A DFT and TD‐DFT Investigation

A series of N‐methyl‐3,4‐fulleropyrrolidine (NMFP) derivatives were designed by selecting different π‐conjugated linkers and electron‐donating groups as D‐π‐A and D‐A systems. The optimised structures and photo‐physical properties of NMFP and its derivatives have been determined using density functional theory (DFT) and time‐dependent density functional theory (TD‐DFT) methods with the B3LYP functional and the 6‐31G basis set. According to the computation analysis, both the π‐conjugated linkers and the electron‐donating groups can influence the electronic and photo‐physical properties of the NMFP derivatives. Our calculated results demonstrated that the electron‐donating groups, with significant electron‐donating ability, had the tendency to increase the highest occupied molecular orbital (HOMO) energy. The π‐conjugated linkers with lower resonance energy decreased the lowest occupied molecular orbital (LUMO) energy and caused a significant decrease in the energy gap (E_g) between the E_HOMO and E_LUMO. A Natural Bond Orbital (NBO) analysis examines the effect of the electron‐donating group, π conjugated linker, and electron‐withdrawing group for these NMFP derivatives. For the NMFP derivatives, a projected density of state (PDOS) analysis demonstrated that the electron density of HOMO and LUMO are concentrated on the electron‐donating group and the π‐conjugated linker, respectively. A TD‐DFT/B3LYP calculation was performed to calculate the electronic absorption spectra of these NMFP derivatives. Both the electron‐donating group and the π‐conjugated linker contribute to the major absorption peaks, which are assigned as HOMO to LUMO transitions and are red‐shifted relative to those of non‐substituted NMFP.     

Reaction energetics on long‐range corrected density functional theory: Diels–Alder reactions

The possibility of quantitative reaction analysis on the orbital energies of long‐range corrected density functional theory (LC‐DFT) is presented. First, we calculated the Diels–Alder reaction enthalpies that have been poorly given by conventional functionals including B3LYP functional. As a result, it is found that the long‐range correction drastically improves the reaction enthalpies. The barrier height energies were also computed for these reactions. Consequently, we found that dispersion correlation correction is also crucial to give accurate barrier height energies. It is, therefore, concluded that both long‐range exchange interactions and dispersion correlations are essentially required in conventional functionals to investigate Diels–Alder reactions quantitatively. After confirming that LC‐DFT accurately reproduces the orbital energies of the reactant and product molecules of the Diels–Alder reactions, the global hardness responses, the halves of highest occupied molecular orbital (HOMO)‐lowest unoccupied molecular orbital (LUMO) energy gaps, along the intrinsic reaction coordinates of two Diels–Alder reactions were computed. We noticed that LC‐DFT results satisfy the maximum hardness rule for overall reaction paths while conventional functionals violate this rule on the reaction pathways. Furthermore, our results also show that the HOMO‐LUMO gap variations are close to the reaction enthalpies for these Diels–Alder reactions. Based on these results, we foresee quantitative reaction analysis on the orbital energies. © 2012 Wiley Periodicals, Inc.     

The effect of conjugated spacer on novel carbazole derivatives for dye‐sensitized solar cells: Density functional theory/time‐dependent density functional theory study

The ground‐state structure and frontier molecular orbital of D‐π‐A organic dyes, CFT1A, CFT2A, and CFT1PA were theoretically investigated using density functional theory (DFT) on B3LYP functional with 6‐31G(d,p) basis set. The vertical excitation energies and absorption spectra were obtained using time‐dependent DFT (TD‐DFT). The adsorptions of these dyes on TiO₂ anatase (101) were carried out by using a 38[TiO₂] cluster model using Perdew–Burke–Ernzerhof functional with the double numerical basis set with polarization (DNP). The results showed that the introduction of thiophene–thiophene unit (T–T) as conjugated spacer in CFT2A could affect the performance of intramolecular charge transfer significantly due to the inter‐ring torsion of T–T being decreased compared with phenylene–phenylene (P–P) spacer of CFP2A in the researhcers' previous report. It was also found that increasing the number of π‐conjugated unit gradually enhanced charge separation between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of these dyes, leading to a high‐efficiency photocurrent generation. The HOMO–LUMO energy gaps were calculated to be 2.51, 2.37, and 2.50 eV for CFT1A, CFT2A, and CFT1PA respectively. Moreover, the calculated adsorption energies of these dyes on TiO₂ cluster were ～14 kcal/mol, implying that these dyes strongly bind to TiO₂ surface. Furthermore, the electronic HOMO and LUMO shapes of all dye–TiO₂ complexes exhibited injection mechanism of electron via intermolecular charge‐transfer transition. © 2012 Wiley Periodicals, Inc.     

Analysis of the Electronic Structure of Aqueous Urea and Its Derivatives: A Systematic Soft X‐Ray–TD‐DFT Approach

Soft X‐ray emission (XE), absorption (XA), and resonant inelastic scattering (RIXS) experiments have been conducted at the nitrogen K‐edge of urea and its derivatives in aqueous solution and were compared with density functional theory and time‐dependent density functional theory calculations. This comprehensive study provides detailed information on the occupied and unoccupied molecular orbitals of urea, thiourea, acetamide, dimethylurea, and biuret at valence levels. By identifying the electronic transitions that contribute to the experimental spectral features, the energy gap between the highest occupied and the lowest unoccupied molecular orbital of each molecule is determined. Moreover, a theoretical approach is introduced to simulate resonant inelastic X‐ray scattering spectra by adding an extra electron to the lowest unoccupied molecular orbital, thereby mimicking the real initial state of the core‐electron absorption before the subsequent relaxation process.     

Molecular design of a π‐conjugated single‐chain electronically conductive polymer

This study demonstrates that single‐chain π‐conjugated systems can be made electrically conductive by modifying the molecular structures of both ends of the oligomers making up a polymer. That is, the highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gaps of a fairly long polyyne‐type oligomer with appropriately modified molecular structures at both ends are found to be on the order of thermal energy by calculations using density functional theory (DFT) with B3LYP functionals. This result applies to molecular structures with characteristic bond alternations. The peculiar bond alternations are caused by competition between two effects of the bond alternations of the two mutually perpendicular π‐conjugated systems, which partially cancel each other out. It is probable that we can design one‐dimensional polymers with HOMO–LUMO gaps small enough to be conductive by combining the above‐mentioned oligomers with each other as monomer units in the polymer. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Ternary Sn‐Ti‐O Electrocatalyst Boosts the Stability and Energy Efficiency of CO2 Reduction

Simultaneously improving energy efficiency (EE) and material stability in electrochemical CO₂ conversion remains an unsolved challenge. Among a series of ternary Sn‐Ti‐O electrocatalysts, 3D ordered mesoporous (3DOM) Sn_0.3Ti_0.7O₂ achieves a trade‐off between active‐site exposure and structural stability, demonstrating up to 71.5 % half‐cell EE over 200 hours, and a 94.5 % Faradaic efficiency for CO at an overpotential as low as 430 mV. DFT and X‐ray absorption fine structure analyses reveal an electron density reconfiguration in the Sn‐Ti‐O system. A downshift of the orbital band center of Sn and a charge depletion of Ti collectively facilitate the dissociative adsorption of the desired intermediate COOH* for CO formation. It is also beneficial in maintaining a local alkaline environment to suppress H₂ and formate formation, and in stabilizing oxygen atoms to prolong durability. These findings provide a new strategy in materials design for efficient CO₂ conversion and beyond.     

Ab initio investigation of 2,2′‐bis(4‐trifluoromethylphenyl)‐5,5′‐bithiazole for the design of efficient organic field‐effect transistors

The initial molecular structure of 2,2′‐bis(4‐trifluoromethylphenyl)‐ 5,5′‐bithiazole has been optimized in the ground state using density functional theory (DFT). The distribution patterns of highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) have also been evaluated. To shed light on the charge transfer properties, we have calculated the reorganization energy of electron λ_e, the reorganization energy of hole λ_h, adiabatic electron affinity (EA_a), vertical electron affinity (EA_v), adiabatic ionization potential (IP_a), and vertical ionization potential (IP_v) using DFT. Based on the evaluation of hole reorganization energy, λ_h, and electron reorganization energy, λ_e, it has been predicted that 2,2′‐bis(4‐trifluoromethylphenyl)‐5,5′‐bithiazole would be a better electron transport material. Finally, the effect of electric field on the HOMO, LUMO, and HOMO–LUMO gap were observed to check its suitability for the use as a conducting channel in organic field‐effect transistors. © 2015 Wiley Periodicals, Inc.     

TbSin(n=2-13)团簇的结构、电子及磁学性质

利用相对论密度泛函理论在广义梯度近似下研究TbSi_n (n=2-13)团簇的结构、稳定性、电子和磁学性质. 对团簇的平均结合能、离解能、电荷转移、最高占据分子轨道(HOMO)和最低未占据分子轨道(LUMO)的能级差、Mulliken 电荷分析和磁学性质进行了计算和讨论. TbSi_n团簇并没有像实验推测的那样在n=10形成嵌入式的结构. 我们推断电子亲和势的急剧变化不仅与嵌入式的结构有关, 而且与电子的固有稳定性相关.Mulliken 电荷分析表明电荷总是从Tb 原子转向Si 原子. 团簇的磁矩主要局域在Tb 原子的周围, 并且主要由f电子贡献, f 电子表现出局域性并且不参与化学成键. 以TbSi₁₀为例的分波态密度分析表明Tb与Si 原子间存在很强的sp轨道杂化.     

5,12‐Diacetyl‐5,12‐dihydroquinoxalino[2,3‐b]quinoxalines: Solid‐State Fluorescence,AIE Properties,and Orbital Switching by Substituent Effect

The compound 5,12‐diacetyl‐5,12‐dihydroquinoxalino[2,3‐b]quinoxaline 1 a and its derivatives were prepared, and their solid‐ and solution‐state spectroscopic properties were studied; 1 a shows stronger fluorescence in solution than in the solid state due to aggregation caused by self‐quenching. Phenyl‐ or alkoxy‐substituted derivatives 1 b – d show solid‐state fluorescence with moderate quantum yields of about Φ=0.12–0.15, although the corresponding values are 0.01–0.07 in solution. The spectroscopic properties of alkoxy‐substituted derivatives were hardly changed compared to 1 a and 1 b , although 1 a and 1 b have similar absorption and fluorescence maxima in solution and in the solid state. DFT calculations indicate that orbital switching occurs between HOMO and HOMO‐1 and HOMO‐2 due to orbital interactions with introduced substituents. Crystal structure analysis revealed that the molecules have bent structures around tertiary nitrogen atoms and form a characteristic dimeric structure.