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.     

Kinetic Study and NBO Analysis of the Dehydrogenation Mechanism of Five‐membered Ring Heterocyclic 2,5‐Dihydro‐[furan,thiophene, selenophene

The theoretical study of the dehydrogenation of 2,5‐dihydro‐[furan ( 1 ), thiophene ( 2 ), and selenophene ( 3 )] was carried out using ab initio molecular orbital (MO) and density functional theory (DFT) methods at the B3LYP/6‐311G**//B3LYP/6‐311G** and MP2/6‐311G**//B3LYP/6‐311G** levels of theory. Among the used methods in this study, the obtained results show that B3LYP/6‐311G** method is in good agreement with the available experimental values. Based on the optimized ground state geometries using B3LYP/6‐311G** method, the natural bond orbital (NBO) analysis of donor‐acceptor (bond‐antibond) interactions revealed that the stabilization energies associated with the electronic delocalization from non‐bonding lone‐pair orbitals [LP(e)_X3] to δ*_{C(1)  H(2)} antibonding orbital, decrease from compounds 1 to 3 . The LP(e)_X3→δ*_{C(1)  H(2)} resonance energies for compounds 1 – 3 are 23.37, 16.05 and 12.46 kJ/mol, respectively. Also, the LP(e)_X3→δ*_{C(1)  H(2)} delocalizations could fairly explain the decrease of occupancies of LP(e)_X3 non‐bonding orbitals in ring of compounds 1 – 3 ( 3 > 2 > 1 ). The electronic delocalization from LP(e)_X3 non‐bonding orbitals to δ*_{C(1)  H(2)} antibonding orbital increases the ground state structure stability, Therefore, the decrease of LP(e)_X3→δ*_{C(1)  H(2)} delocalizations could fairly explain the kinetic of the dehydrogenation reactions of compounds 1 – 3 (k ₁ >k ₂ >k ₃ ). Also, the donor‐acceptor interactions, as obtained from NBO analysis, revealed that the (_C(4)C(7)→δ*_{C(1)  H(2)} resonance energies decrease from compounds 1 to 3 . Further, the results showed that the energy gaps between (_C(4)C(7) bonding and δ*_{C(1)  H(2)} antibonding orbitals decrease from compounds 1 to 3 . The results suggest also that in compounds 1 – 3 , the hydrogen eliminations are controlled by LP(e)→δ* resonance energies. Analysis of bond order, natural bond orbital charges, bond indexes, synchronicity parameters, and IRC calculations indicate that these reactions are occurring through a concerted and synchronous six‐membered cyclic transition state type of mechanism.     

High Magnetic Moments in Manganese‐Doped Silicon Clusters

We report on the structural, electronic, and magnetic properties of manganese‐doped silicon clusters cations, Si_nMn⁺ with n=6–10, 12–14, and 16, using mass spectrometry and infrared spectroscopy in combination with density functional theory computations. This combined experimental and theoretical study allows several structures to be identified. All the exohedral Si_nMn⁺ (n=6–10) clusters are found to be substitutive derivatives of the bare Si_n+1⁺ cations, while the endohedral Si_nMn⁺ (n=12–14 and 16) clusters adopt fullerene‐like structures. The hybrid B3P86 functional is shown to be appropriate in predicting the ground electronic states of the clusters and in reproducing their infrared spectra. The clusters turn out to have high magnetic moments localized on Mn. In particular the Mn atoms in the exohedral Si_nMn⁺ (n=6–10) clusters have local magnetic moments of 4 μ_B or 6 μ_B and can be considered as magnetic copies of the silicon atoms. Opposed to other 3d transition‐metal dopants, the local magnetic moment of the Mn atom is not completely quenched when encapsulated in a silicon cage.     

Theoretical Study on Gas—phase Pyrolytic Reactions of N—Ethyl,Isopropyl and N—t—Butyl Substituted 2—Aminopyrazine

Density functional theory (DFT) and ab initio methods were used to study gas‐phase pyrolytic reaction mechanisms of iV‐ethyl, N‐isopropyl and N‐t‐butyl substituted 2‐aminopyrazine at B3LYP/6–31G* and MP2/6–31G*, respectively. Single‐point energies of all optimized molecular geometries were calculated at B3LYP/6–311 + G(2d,p) level. Results show that the pyrolytic reactions were carried out through a unimolecular first‐order mechanism which were caused by the migration of atom H(17) via a six‐member ring transition state. The activation energies which were verified by vibrational analysis and correlated with zero‐point energies along the reaction channel at B3LYP/6–311 + G(2d,p) level were 252.02 kJ. mo^?1 (N‐ethyl substituted), 235.92 kJ‐mol^?1 (N‐t‐isopropyl substituted) and 234.27 kJ‐mol^?1 (N‐t‐butyl substituted), respectively. The results were in good agreement with available experimental data.     

Tetra- and hexaatomic cyclic clusters of main-group elements (XY)2 and (XY)3: an ab initio and density functional study

The electronic and molecular structure of planar (cyclic and linear) tetra- and hexaatomic clusters (XY) _n (XY = CC, BN, BeO, LiF; n = 2, 3) was studied using the ab initio CCD(full)/6-311+G** method and density functional approach (B3LYP/6-311+G**). The stability of cyclic clusters C₆, B₃N₃, and Be₃O₃ with D_3h symmetry is mainly determined by the aromaticity of their -electron systems.     

Pyridine adsorption on small Nin‐cluster (n = 2,3,4): A study of geometry and electronic structure

Adsorption of pyridine on Ni_n‐clusters (with n = 2,3,4) is studied by quantum chemical calculations at B3LYP/LANL2DZ and B3LYP/6‐311G^** levels. First, Ni_n‐clusters are investigated for accessible structure and electronic states. The lowest electronic state with four unpaired electrons is predicted for Ni₄‐cluster based on geometry and electronic structure, showing that the cluster stability nicely depends on number of unpaired electrons. Correction for basis set superposition error of metal‐metal bond is appreciable and has increasing effect on cluster binding energy. Next, adsorption of pyridine in planar and vertical adsorption modes is investigated on rhombus Ni₄‐cluster. The vertical mode is found (at B3LYP/6‐311G^** level) as the most favorable adsorption mode. Adsorption energy (ΔE_ads) depends on cluster size; adsorption on Ni₄‐cluster is most favorable with ΔE_ads = ?207.33 kJ/mol. The natural bond orbital analysis reveals the charge transfer in adsorbate/metal‐cluster. Results of investigations for the Ni₂‐ and Ni₃‐cluster are also presented. © 2012 Wiley Periodicals, Inc.     

Comparison of density functionals for the study of the high spin low spin gap in Fe(III) spin crossover complexes

A detailed investigation of the accuracy of different quantum mechanical methods for the study of iron(III) spin crossover complexes is presented. The energy spin state gap between the high and low spin states; ΔE (HS‐LS) of nine iron(III) quinolylsalicylaldiminate complexes were calculated with nine different DFT functionals, then compared. DFT functionals: B3LYP, B3LYP‐D3, B3LYP*, BH&HLYP, BP86, OLYP, OPBE, M06L, and TPSSh were tested with six basis sets: 3‐21G*, dgdzvp, 6‐31G**, cc‐pVDZ, Def2TZVP, and cc‐pVTZ. The cations from the X‐ray crystal structures of [Fe(qsal‐OMe)₂]Cl·MeCN·H₂O, [Fe(qsal‐OMe)₂]Cl·2MeOH·0.5H₂O, [Fe(qsal‐OMe)₂]BF₄·MeOH, [Fe(qsal‐OMe)₂]NCS·CH₂Cl₂, [Fe(qsal‐F)₂]NCS, [Fe(qsal‐Cl)₂]NCS·MeOH, [Fe(qsal‐Br)₂]NCS·MeOH, [Fe(qsal‐I)₂]OTf·MeOH, and [Fe(qsal)₂]NCS?CH₂Cl₂ were used as starting structures. The results show that B3LYP, B3LYP‐D3, OLYP, and OPBE with a 6‐31G**, Def2TZVP, and cc‐pVTZ basis set give reasonable results of ΔE (HS‐LS) compared with the experimental data. The enthalpy of [Fe(qsal‐I)₂]⁺ calculated with an OLYP functional and cc‐pVTZ basis set (1.48 kcal/mol) most closely matches the experimental data (1.34 kcal/mol). B3LYP* yields an enthalpy of 5.92 kcal/mol suggesting it may be unsuitable for these Fe(III) complexes, mirroring recent results by Kepp (Inorg . Chem ., 2016, 55 , 2717–2727).     

PO → Si intramolecular coordination in the derivatives of 1,4‐phosphasilacyclohexane 1‐oxides

The chair and boat conformers for a series of derivatives of 1,4‐phosphasilacyclohexane 1‐oxides have been calculated at the B3LYP/6‐311+G** level of theory in the gas phase and taking into account the effect of solvent polarity using the IEF‐PCM model. The stability of the boat conformers containing pentacoordinate silicon due to formation of the P?O→Si intramolecular coordination bond depends on the environment of the phosphorus atom and polarity of the solvent, and the strength of the transannular bond depends also on the nature of the substituents at the silicon atom. The highly polar boat conformers are strongly stabilized in the DMSO solution. NBO analysis showed the importance of the σ(C? Si) → σ*(H₃C? N) hyperconjugative interaction in the two H₃C? N? C? Si fragments of the ring favoring the formation of the pentacoordinate silicon atom. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Absorption spectra of azobenzenes simulated with time‐dependent density functional theory

Using time‐dependent density functional theory and the polarizable continuum model, we have simulated the absorption spectra of an extended series of azobenzene dyes. First, we have determined a theoretical level optimal for this important class of dyes, and it turned out that a C‐PCM‐CAM‐B3LYP/6‐311+G(d,p)//C‐PCM‐B3LYP/6‐311G(d,p) approach represents an effective compromise between chemical accuracy and computational cost. In a second stage, we have compared the theoretical and experimental transition energies for 46 n → π^☆ and 141 π → π^☆ excitations. For the full set, that spans over a 302–565 nm domain, we obtained a mean absolute deviation of 13 nm (0.10 eV) and a linear correlation coefficient of 0.95, illustrating the accuracy of our approach, though some significant outliers pertained. In a last step, the impact of several modifications, that is, trans/cis isomerization, variation of the acidity of the medium and azo/hydrazo tautomerism have been modeled with two functionals. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Excited state properties,fluorescence energies,and lifetimes of a poly(fluorene‐phenylene), based on TD‐DFT investigation

The structural and electronic properties of fluorene‐phenylene copolymer (FP)_n, n = 1–4 were studied by means of quantum chemical calculations based on density functional theory (DFT) and time dependent density functional theory (TD‐DFT) using B3LYP functional. Geometry optimizations of these oligomers were performed for the ground state and the lowest singlet excited state. It was found that (FP)_n is nonplanar in its ground state while the electronic excitations lead to planarity in its S₁ state. Absorption and fluorescence energies were calculated using TD‐B3LYP/SVP and TD‐B3LYP/SVP+ methods. Vertical excitation energies and fluorescence energies were obtained by extrapolating these values to infinite chain length, resulting in extrapolated values for vertical excitation energy of 2.89 and 2.87 eV, respectively. The S₁ ← S₀ electronic excitation is characterized as a highest occupied molecular orbital to lowest unoccupied molecular orbital transition and is distinguishing in terms of oscillator strength. Fluorescence energies of (FP)_n calculated from TD‐B3LYP/SVP and TD‐B3LYP/SVP+ methods are 2.27 and 2.26 eV, respectively. Radiative lifetimes are predicted to be 0.55 and 0.51 ns for TD‐B3LYP/SVP and TD‐B3LYP/SVP+ calculations, respectively. These fundamental information are valuable data in designing and making of promising materials for LED materials. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

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     

Computational study of tautomerism and aromaticity in mono‐ and dithio‐substituted tropolone

Keto‐enol tautomerism in mono‐ and dithio‐substituted analogs of tropolone was investigated using electronic structure computations. Seven structural isomers of C₇H₆OS and four of C₇H₆S₂ were optimized fully in gas phase at HF and B3LYP theoretical levels in combination with the 6‐311++g** basis set, as well as with the CBS‐QB3 and G3 methods. To examine the effects of an aqueous solvent on tautomeric equilibrium constants, each species was optimized in water using the self‐consistent reaction field polarizable continuum model at HF/6‐311++g** and B3LYP/6‐311++g** model chemistries. In both phases it was found that the enol forms were significantly more stable with respect to electronic energy and Gibbs free energy compared to the keto isomers, and outnumbered the keto species by several orders of magnitude. This was understood on the basis of elementary Hückel theory and the 4n + 2 rule, and supported by nucleus independent chemical shifts computations of NMR chemical shifts in these seven membered cyclic systems. © 2012 Wiley Periodicals, Inc.     

Geometry,stability, and isomerization of BnN2 (n = 1−6) isomers

We perform a systematic study on the geometry, stability, nature of bonding, and potential energy surface of low‐lying isomers of planar and cyclic B_nN₂ (n = 1?6) at the CCSD(T)/6‐311+G(d)//B3LYP/6‐311+G(d) level. B_nN₂ (n = 2?4) clusters are structurally similar to pure boron clusters. The evolution of the binding energy per atom, incremental binding energy, and second‐order difference of total energy with the size of B_nN₂ reveals that the lowest energy isomer of B₃N₂ has high stability. B₅N₂ and B₆N₂ possess π‐aromaticity according to Hückel (4n + 2) rule. The aromaticity of some isomers of B₄N₂ and B₆N₂ is examined based on their valence molecular orbitals. At the CCSD(T)/6‐311+G(d)//B3LYP/6‐311+G(d) level, several B₂N₂, B₃N₂, B₄N₂, and B₅N₂ isomers are predicted to be stable both thermodynamically and kinetically, and detectable in future experiments. © 2013 Wiley Periodicals, Inc.     

The effect of silicon doping on the geometrical structures,stability, and electronic and spectral properties of magnesium clusters: DFT study of SiMgn (n = 1-12) clusters

Using the density functional theory (DFT) method at the B3LYP /6−311G (D) level, we studied how silicon doping affects the geometrical structure, stability, and electronic and spectral properties of magnesium clusters. The stable isomers of SiMg _n (n = 1-12) clusters were calculated by searching numerous initial configurations using the CALYPSO program. The geometrical structure optimization shows that most stable SiMg _n (n = 3-12) clusters are three-dimensional. In addition, geometrical structure growth patterns show that some structures of SiMg _n clusters can be directly formed by replacing one Mg atom in the corresponding Mg _{n + 1} cluster with one silicon atom, such as SiMg₈ and Mg₉ clusters. The stability of SiMg _n clusters is analyzed by calculating the average binding energy, fragmentation energy, and second-order energy difference. The results show that SiMg _n clusters with n = 5 and 8 are more stable than others. MO contents analysis show that the Si 3p-orbitals and Mg 3s-orbital are mainly responsible for the stability of these two clusters. The results of the natural charge population (NCP) and natural electronic configure (NEC) analysis of the electronic properties reveal that the charges in SiMg_n (n = 1-12) clusters transfer from magnesium atoms to silicon frame, and electronic charge distributions are primarily governed by s- and p-orbital interactions. In addition, the Vertical ionization potential (VIP), vertical electron affinity (VEA), and chemical hardness of ground sates of SiMg _n (n = 1-12) clusters were studied in detail and compared with the experimental results. The conclusions show that the chemical hardness of most SiMg _n clusters are lower than that of pure Mg _{n + 1} (n = 1-12) clusters, except for n = 1 and 8. This indicates that the doping of silicon atom can always reduce the chemical hardness of pure magnesium clusters. Finally, the infrared and Raman spectral properties of SiMg₅ and SiMg₈ clusters were calculated and discussed in detail.     

Chemical Reactivity of Oxo‐ and Aza‐γ‐lactam Rings

Different mechanisms for the alkaline hydrolysis of oxo and aza‐γ‐lactam rings have been studied by ab initio calculations at the MP2/6‐31+G*//MP2/6‐31+G* and B3LYP/6‐31+G*//B3LYP/6‐31+G* levels. The tetrahedral intermediate can undergo two different reactions, the cleavage of the C₂−N₂ bond (the classical mechanism) and the cleavage of the C₂−X₆ bond (X=O, N). Both compounds present similar energy barriers for the classical fragmentation, and show considerably lower barriers for the alternative mechanism. Because of this reactivity, the compounds studied are expected to be β‐lactamase inhibitors.     

Intermolecular interactions of a size‐expanded guanine analogue with gold nanoclusters

The interactions between a size‐expanded Guanine analogue x‐Guanine (xG) and gold nanoclusters, Au_n (n = 2, 4, 6, and 8), were studied theoretically using density functional theory. Geometries of neutral complexes were optimized using the B3LYP functional with the 6‐31+G(d,p) basis set for xG and the LANL2DZ basis set for gold clusters. The binding modes, interaction strength, and the charge‐transfer properties of different Au_n‐xG complexes were investigated. Natural population analysis was performed for natural bond order charges. It was found that gold nanoclusters form stable complexes with xG and these binding results in a substantial amount of electronic charge being transferred from xG to the gold clusters. The vertical first ionization potential, electron affinity, Fermi Level, and the HOMO–LUMO gap of xG and its complexes with gold nanoclusters were also analyzed. © 2013 Wiley Periodicals, Inc.     

The Geometric Structure of Silver‐Doped Silicon Clusters

Cationic silver‐doped silicon clusters, Si_nAg⁺ (n=6–15), are studied using infrared multiple photon dissociation in combination with density functional theory computations. Candidate structures are identified using a basin‐hopping global optimizations method. Based on the comparison of experimental and calculated IR spectra for the identified low‐energy isomers, structures are assigned. It is found that all investigated clusters have exohedral structures, that is, the Ag atom is located at the surface. This is a surprising result because many transition‐metal dopant atoms have been shown to induce the formation of endohedral silicon clusters. The silicon framework of Si_nAg⁺ (n=7–9) has a pentagonal bipyramidal building block, whereas the larger Si_nAg⁺ (n=10–12, 14, 15) clusters have trigonal prism‐based structures. On comparing the structures of Si_nAg⁺ with those of Si_nCu⁺ (for n=6–11) it is found that both Cu and Ag adsorb on a surface site of bare Si_n⁺ clusters. However, the Ag dopant atom takes a lower coordinated site and is more weakly bound to the Si_n⁺ framework than the Cu dopant atom.     

Scaling factors for vibrational frequencies and zero-point vibrational energies of some recently developed exchange-correlation functionals

The scaling factors for the vibrational frequencies and zero-point vibrational energies evaluated at various combinations of recently developed exchange-correlation functionals and various basis sets are reported. The exchange-correlation functionals considered are B972, B98, HCTH, OLYP, O3LYP, G96LYP, PBE0 and VSXC functionals; the basis sets employed are 3-21G, 6-31G*, 6-31G**, 6-31+G, 6-311G*, 6-311G**, 6-311G(df,p), 6-311+G(df,p), cc-pVDZ and aug-cc-pVDZ. The experimental harmonic frequencies of 122 small molecules and the zero-point vibrational energies of 39 small molecules are used to determine the scaling factors through the least-square fitting procedure. It was found that the scaling factors do not depend significantly on the basis sets considered. The vibrational frequency scaling factors evaluated by using the B98 and PBE0 functionals are recommended on the basis of smallest root mean square error. The zero-point vibrational energy scaling factors evaluated from the B972 functional with Pople's double-zeta basis set and the HCTH functional with Pople's triple-zeta basis set are recommended on the basis of smallest root mean square error.     

Density functional theoretical study of pKa of RCOOH (RH,CH3, and C2H5) using the combination of the extended clusters‐continuum model

The accurate pK_a determinations for three carboxylic acids have been investigated using the combination of the extended clusters‐continuum model at B3LYP/6‐31+g(d,p) and B3LYP/6‐311++g(d,p) levels. To take into account of the effect of the water combined with carboxylic acids in different positions, eleven molecular clusters were considered. Among these clusters, the one involving the carboxylic acid wrapped up with water molecules and saturated with hydrogen bonds (four hydrogen bonds around ? COOH) leads to the best B3LYP pK_a results compared to the experimental data. For those clusters saturated with hydrogen bonds, when n = 3 (the number of water molecules), the average absolute errors between the calculated pK_a results and experimental data of these three carboxylic acids were 0.19 (0.23) and 0.12 (0.22) pK_a at B3LYP/6‐31+g(d,p)//PCM (IEFPCM) and B3LYP/6‐311++g(d,p)//PCM (IEFPCM) levels, respectively; when n = 4, they are 0.53 (1.23) and 1.09 (1.03) pK_a, respectively. On the basis of the above results, the molecular cluster saturated with four hydrogen bonds formed by three waters and one carboxylic acid molecule was the chief existence in the carboxylic acid solution. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012