Blue and red shifts in Rg···HCN and Rg···HNC complexes (Rg=He,Ne, Ar,Kr)

The shift in the harmonic vibrational frequency of the H–C stretch of HCN on formation of the linear Rg···HCN complexes, and of the H–N stretch of HNC on the formation of Rg···HNC complexes (Rg?=?He, Ne, Ar, Kr), has been determined by ab initio computations. These shifts are in agreement with predictions from a model based on perturbation theory and involving the first and second derivatives of the interaction energy with respect to displacement of the H–C (H–N) bond length from its equilibrium value in the monomer. Small blue shifts were obtained for He···HCN, Ne···HCN and He···HNC, while red shifts were obtained for the other weakly bound complexes. These vibrational characteristics are rationalized by considering the balance between the interaction energy derivatives obtained from the perturbative model. For all complexes, the IR intensity of the H–C or H–N stretch was increased from the isolated monomer values on complexation.     

Strengthening of the halogen-bonding by an aerogen bond interaction: substitution and cooperative effects in O3Z···NCX···NCY (Z = Ar,Kr, Xe; X = Cl,Br, I; Y = H,F, OH) complexes

The geometry, interaction energy and bonding properties of ternary complexes O₃Z···NCX···NCY (Z= Ar, Kr, Xe; X = Cl, Br, I and Y = H, F, OH) are investigated with ab initio calculations at the MP2/aug-cc-pVTZ level. Two different types of intermolecular interactions are present in these complexes, namely, aerogen bond (Z···N) and halogen bond (X···N). The formation mechanism and bonding properties of these complexes are analysed with molecular electrostatic potentials, quantum theory of atoms in molecules and non-covalent interaction index. It is found that the cooperativity energies in the ternary complexes are all negative; that is, the interaction energy of the ternary complex is greater (more negative) than the sum of the interaction energies of the corresponding binary systems. Also, the cooperativity energies increase with the increase of the interaction energies. The cooperative effects in the ternary complexes make a decrease in the total spin–spin coupling constants across the aerogen bonding, J(Z–N), which can be regarded as a proof for the reinforce of Z···N interactions in the ternary complexes with respect to the binary systems.     

Electron spin resonance and structure of the ionic radical, ·PO3 =

It is shown that the ionic radical, ·PO₃ ⁼, is formed by the action of γ-rays on disodium ortho-phosphite pentahydrate. The hyperfine coupling to the ³¹P nucleus has principal values of 1967, 1514 and 1513 Mc/s and is consistent with a pyramidal ion having OPO angles of 110°.     

Cooperative interaction between π-hole and single-electron σ-hole interactions in O2S···NCX···CH3 and O2Se···NCX···CH3 complexes (X = F,Cl, Br and I)

Ab initio calculations are performed to analyse the cooperative effects between π-hole and single-electron σ-hole interactions in O₂S···NCX···CH₃ and O₂Se···NCX···CH₃ complexes, where X = F, Cl, Br and I. These effects are investigated in terms of geometric and energetic features of the complexes, which are computed by UMP2/aug-cc-pVTZ(-PP) method. Our results indicate that the shortening of the each π-hole bond distance in the complexes is dependent on the strength of the σ-hole interaction. The maximum and minimum energetic cooperativity values correspond to the most and least stable complexes studied in the present work. The cooperativity between both types of interaction is chiefly caused by the electrostatic effects. The topological analysis, based on the quantum theory of atoms in molecules, is used to characterise the interactions and analyse their enhancement with varying electron density at bond critical points.     

Birkhoff’s Polytope and Unistochastic Matrices,N = 3 and N = 4

The set of bistochastic or doubly stochastic N×N matrices is a convex set called Birkhoff’s polytope, which we describe in some detail. Our problem is to characterize the set of unistochastic matrices as a subset of Birkhoff’s polytope. For N=3 we present fairly complete results. For N=4 partial results are obtained. An interesting difference between the two cases is that there is a ball of unistochastic matrices around the van der Waerden matrix for N=3, while this is not the case for N=4.     

Prediction and characterisation of a chalcogen···π interaction with acetylene as a potential electron donor in XHS···HCCH and XHSe···HCCH (X = F,Cl, Br,CN, OH,OCH3, NH2, CH3) σ-hole complexes

It is well-known that many covalently bonded atoms of group VI have specific positive regions of electrostatic potential (σ-holes) through which they can interact with Lewis bases. This interaction is called ‘chalcogen bond’ by analogy with halogen bond and hydrogen bond. In this study, ab initio calculations are performed to predict and characterise chalcogen···π interactions in XHS···HCCH and XHSe···HCCH complexes, where X = F, Cl, Br, CN, OH, OCH₃, NH₂, CH₃. For the complexes studied here, XHS(Se) and HCCH are treated as a Lewis acid and a Lewis base, respectively. The CCSD(T)/aug-cc-pVTZ interaction energies of this type of σ-hole bonding range from ?1.18 to ?4.83 kcal/mol. The calculated interaction energies tend to increase in magnitude with increasing positive electrostatic potential on the extension of X–S(Se) bond. The stability of chalcogen···π complexes is attributed mainly to electrostatic and correlation effects. The nature of chalcogen···π interactions is unveiled by means of the atoms in molecules, natural bond orbital, and electron localisation function analyses.     

Interplay and competition between the lithium bonding and halogen bonding: R3C···XCN···LiCN and R3C···LiCN···XCN as a working model (R = H,CH3; X = Cl,Br)

UMP2 calculations with aug-cc-pVDZ basis set were used to analyse intermolecular interactions in R₃C···XCN···LiCN and R₃C···LiCN···XCN triads (R = H, CH₃; X = Cl, Br) which are connected via lithium bond and halogen bond. To understand the properties of the systems better, the corresponding dyads are also studied. Molecular geometries and binding energies of dyads, and triads are investigated at the UMP2/aug-cc-pVDZ computational level. Particular attention is paid to parameters such as cooperative energies, and many-body interaction energies. All studied complexes, with the simultaneous presence of a lithium bond and a halogen bond, show cooperativity with energy values ranging between ?1.20 and ?7.71 kJ mol^?1. A linear correlation was found between the interaction energies and magnitude of the product of most positive and negative electrostatic potentials (V_S,maxV_S,min). The electronic properties of the complexes are analysed using parameters derived from the atoms in molecules (AIM) methodology. According to energy decomposition analysis, it is revealed that the electrostatic interactions are the major source of the attraction in the title complexes.     

Cooperativity effects between σ-hole interactions: a theoretical evidence for mutual influence between chalcogen bond and halogen bond interactions in F2S···NCX···NCY complexes (X = F,Cl, Br,I; Y = H,F, OH)

Quantum chemical calculations are performed to study the cooperativity effects between chalcogen bond and halogen bond interactions in F₂S···NCX···NCY complexes, where X = F, Cl, Br, I and Y = H, F, OH. These effects are investigated in terms of geometric and energetic features of the complexes, which are computed by second-order Møller–Plesset perturbation theory (MP2). For each F₂S···NCX···NCY complex studied, the effect of cooperativity on the chalcogen bond is dependent on the strength of halogen bond. The results indicate that the interaction energies of chalcogen and halogen bonds in the triads are more negative relative to the respective dyads. The interaction energy of chalcogen bond is increased by 31%–49%, whereas that of halogen bond by 28%–62%. The energy decomposition analysis reveals that electrostatic force plays a main role in the cooperativity effects between the chalcogen bond and halogen bond interactions. The topological analysis, based on the quantum theory of atoms in molecules, is used to characterise the interactions and analyse their enhancement with varying electron density at bond critical points.     

A theoretical analysis of the weakly bound complexes HM ··· HXY (M=O and S; XY=CN and NC): comparison with H2M ··· HXY complexes

An ab initio study of the complexes formed between MH (M=O and S) and HXY (XY=CN and NC) was carried out at the UQCISD/6-311++G(2df,2p) level. For comparison, the corresponding H₂M–HXY complexes were also studied. Two minima were found for each molecular pair. The results show the necessity of electron correlation and larger basis sets in the study of open-shell hydrogen-bonded complexes. As the proton donor and acceptor, the OH radical is favourable for the formation of a hydrogen bond with HXY than is the SH radical. The MH radical is more likely to donate a proton than H₂M, whereas H₂M is more likely to accept a proton than the MH radical. Natural bond orbital and atoms in molecules analyses were performed for these systems. It is shown that the complexes are held together mainly by electrostatic interactions.     

Magnetocaloric effects in RT X intermetallic compounds(R = Gd–Tm,T = Fe–Cu and Pd,X = Al and Si)

The magnetocaloric effect(MCE) of RT Si and RT Al systems with R = Gd–Tm, T = Fe–Cu and Pd, which have been widely investigated in recent years, is reviewed. It is found that these RT X compounds exhibit various crystal structures and magnetic properties, which then result in different MCE. Large MCE has been observed not only in the typical ferromagnetic materials but also in the antiferromagnetic materials. The magnetic properties have been studied in detail to discuss the physical mechanism of large MCE in RT X compounds. Particularly, some RT X compounds such as Er Fe Si,Ho Cu Si, Ho Cu Al exhibit large reversible MCE under low magnetic field change, which suggests that these compounds could be promising materials for magnetic refrigeration in a low temperature range.     

Enhancement effect of lithium bonding on the strength of pnicogen bonds: XH2P···NCLi···NCY as a working model (X = F,Cl; Y = H,F, Cl,CN)

MP2 calculations with aug-cc-pVDZ basis set were used to analyse intermolecular interactions in XH₂P···NCLi···NCY triads (X = F, Cl; Y = H, F, Cl, CN) which are connected via pnicogen bond and lithium bond. To understand the properties of the systems better, the corresponding dyads are also studied. Molecular geometries and interaction energies of dyads, and triads are investigated at the MP2/aug-cc-pVDZ computational level. Particular attention is paid to parameters such as cooperative energies and many-body interaction energies. All studied complexes, with the simultaneous presence of a lithium bond and a pnicogen bond, show cooperativity with energy values ranging between ?4.73 and ?8.88 kJ mol^?1. A linear correlation was found between the interaction energies and magnitude of the product of most positive and negative electrostatic potentials. According to energy decomposition analysis, it is revealed that the electrostatic interactions are the major source of the attraction in the title complexes.     

Electronic structure and magnetic properties of RCo5−xMx (R=Y,Pr and M=Al,Si) system

Detailed theoretical and experimental investigations of the electronic and magnetic properties of the RCo_5?xM_x compounds (R=Y, Pr and M=Si, Al) have been performed. All theoretical investigations of the electronic and magnetic properties of the system have been done using the Korringa–Kohn–Rostoker (KKR) band structure method. The Si for Co substitution in RCo₅ does not change the magnetic ordering: the RCo_5?xSi_x with R=Y, Nd and Pr is ferromagnetic, whilst the heavy rare-earth containing compounds are ferrimagnetic. The important modifications induced by this substitution concerns the magnetic properties of the system: the Curie temperature and the magnetic moments of Co decrease with Si content, indicating the weakening of the Co–Co exchange interaction. The band structure calculations evidence the hybridization between the 3d electronic states of Co and the 3p states of Si as possible reason for the diminishing of Co–Co exchange interaction. Also, the volume effect on the magnetic properties of the YCo₄Si was investigated using theoretical methods. The results are compared with the experimental measurements in order to distinguish the origin of magnetization reduction in YCo₄Si compared with YCo₄Al.     

A computational study of interplay between hydride bonding and cation–π interactions: H-Mg-H···X···Y triads (X = Li+, Na+, Y = C2H2, C2H4, C6H6) as model systems

In the present study, H-Mg-H···X···Y (X = Li⁺, Na⁺ and Y = C₂H₂, C₂H₄, C₆H₆) triads have been investigated at MP2/6-311++G(2d,2p) computational level to characterise cooperative effects between hydride bonding and cation–π interactions. Molecular geometries, binding energies, cooperative energies and many-body interaction energies were evaluated. The diminutive energy values in triads with Li⁺ are larger than respective values in triads with Na⁺. The electronic properties of the complexes are analysed using parameters derived from the quantum theory of atoms in molecules methodology.     

Cooperativity between the hydrogen bonding and halogen bonding in F3CX ··· NCH(CNH) ··· NCH(CNH) complexes (X=Cl,Br)

MP2 calculations with the cc-pVTZ basis set were used to analyse the intermolecular interactions in F₃CX?···?NCH(CNH)?···?NCH(CNH) triads (X=Cl, Br), which are connected via hydrogen and halogen bonds. Molecular geometries, binding energies, and infrared spectra of the dyads and triads were investigated at the MP2/cc-pVTZ computational level. Particular attention was given to parameters such as the cooperative energies, cooperative dipole moments, and many-body interaction energies. All studied complexes, with the simultaneous presence of a halogen bond and a hydrogen bond, show cooperativity with energy values ranging between ?1.32 and ?2.88?kJ?mol^?1. The electronic properties of the complexes were analysed using the Molecular Electrostatic Potential (MEP), electron density shift maps and the parameters derived from the Atoms in Molecules (AIM) methodology.     

Crystal structures, phase relationships, and magnetic phase transitions of RsM4 compounds （R = rare earths, M = Si, Ge）

Our recent studies of the crystal structures, phase transitions, and magnetic properties of intermetallic compounds RsM4 （R = rare earths; M = Si, Ge） are reviewed briefly. First, crystal structures, phase relationships, and magnetic prop- erties of several 5：4 compounds, including Nd5 Si4-xGex, Pr5 Si4_xGex, Gds-xLaxGe4, La5 Si4, and Gd5 Sn4, are presented. In particular, the canted spin structures as well as the magnetic phase transitions in PrsSi2Ge2 and PrsGe4 investigated by neutron powder diffractions and small-angle neutron scattering are reviewed. Second, the crystal structures and magnetic properties of the most studied compounds Gds（Si,Ge）4 are summarized. The focus is on the parent compound GdsGe4, which is an amazing material exhibiting magnetic anisotropy, angular dependent spin-flop transition, metastable magnetic response, Griffiths-like phase, thermal effect under pulsed fields, antiferromagnetic and ferromagnetic resonances, pro- nounced effects of impurities, and high-field induced magnetic transitions.     

Structures and stabilities of the donor–acceptor complexes HXPY (X=Al,B; Y=H,F, OH)

The optimized geometries, complexation energies, etc. of HXPY (X?=?Al, B; Y?=?H, F, OH) donor–acceptor complexes have been investigated at the B3LYP/6-311+G(d,p), MP2/6-311+G(d,p) and/or CCSD(T)/6-311+G(d,p) levels. The results show that HBPY (Y?=?H, F, OH) is more stable than the corresponding HAlPY (Y?=?H, F, OH), F (or OH) substitution on phosphorus results in decreasing complex stability, and the stronger the electron-attracting nature of the substitution atom, the more stable the complex. Moreover, the thermodynamic and kinetic properties of the formation reaction of these donor–acceptor complexes were also examined within the temperature range 200–800?K using the general statistical thermodynamics and Eyring transition state theory with Wigner correction. It is concluded that the formation of HBPY is thermodynamically favoured over that of the corresponding HAlPY, especially at low temperature, and is kinetically favoured over that of the relevant HAlPY (Y?=?H, F, OH), especially at high temperature.     

A comparative study on geometries,stabilities, and electronic properties between bimetallic AgnX（X=Au,Cu;n=1-8）and pure silver clusters

Using the meta-generalized gradient approximation (meta-GGA) exchange correlation TPSS functional, the geo- metric structures, the relative stabilities, and the electronic properties of bimetallic Ag n X (X=Au, Cu; n=1–8) clusters are systematically investigated and compared with those of pure silver clusters. The optimized structures show that the transition point from preferentially planar to three-dimensional structure occurs at n = 6 for the Ag n Au clusters, and at n = 5 for Ag n Cu clusters. For different-sized Ag n X clusters, one X (X=Au or Cu) atom substituted Ag n+1 structure is a dominant growth pattern. The calculated fragmentation energies, second-order differences in energies, and the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) energy gaps show interesting odd–even oscillation behaviours, indicating that Ag 2,4,6,8 and Ag 1,3,5,7 X (X=Au, Cu) clusters keep high stabilities in comparison with their neighbouring clusters. The natural population analysis reveals that the charges transfer from the Ag n host to the impurity atom except for the Ag 2 Cu cluster. Moreover, vertical ionization potential (VIP), vertical electronic affinity (VEA), and chemical hardness (η) are discussed and compared in depth. The same odd–even oscillations are found for the VIP and η of the Ag n X (X=Au, Cu; n=1–8) clusters.     

The prominent enhancing effect and mechanism of the methyl group in the X···Y (X=O,S, H3CO,H3CS, (H3C)2O, (H3C)2S; Y=HCN,HNC) hydrogen-bonded complex

An ab initio computational study of the enhancing role of the methyl group in the M···H (M=S and O) hydrogen bond has been carried out at the QCISD/6-311++G(2df,2p) level. The bond lengths, frequency shifts, and interaction energies were analysed. The methyl group of the electron donor plays a positive role in the formation of the hydrogen bond. Its enhancing role is stronger in the O···H hydrogen bond than in the S···H hydrogen bond. The results show that the methyl group has a prominent effect on the strength of the hydrogen bond. The interaction energy is increased by 347% for the Me₂O–HCN complex relative to that for the O–HCN complex. The enhancing mechanism of the methyl group has been analysed by means of natural bond orbital (NBO) theory. The electrostatic interaction is of more importance to the O···H hydrogen bond, whereas dispersion and charge-transfer interactions play a more significant role in the S···H hydrogen bond.     

Substituent effects on gas-phase acidities of formic acid and its silicon and sulphur derivatives R − M(= X)XH(M = C., Si; X = O,S; R = H,F, CI,OH, NH2 and CH3)

Ab initio molecular orbital methods at the CBS-Q level of theory have been used to study the effect of substituent (F, Cl, NH₂, OH and CH₃) on the gas-phase acidities of formic acid, HCOOH, its silicon and sulphur derivatives R-M(= X)XH(M = C., Si; X = 0, S; R = F, Cl, OH, NH₂ and CH₃). For formic acid and its thio and dithio derivatives the acidity changes upon substitution are irregular and depend on both the type of substituent, position and degree of replacement of oxygen atoms by sulphur atoms. For sila carboxylic acids and their thio and dithio derivatives the calculated acidities regularly increase in the order: R-SiOOH < R-Si(=S)OH ? R-Si(=O)SH < R-SiSSH(R = H, F, Cl, OH, NH₂ and CH₃). The chloro derivatives are the strongest among the acids studied. The highest gas phase acidity (1277.6 kJmol^?1) has been calculated for ClC(=S)OH.