The σ-hole of M2 H6 (M = Al, Ga, In) and π-hole of MH3 (M = Al, Ga, In) were discovered and analyzed, the bimolecular complexes M2 H6 ···NH3 and MH3 ···N2 P2 F4 (M = Al, Ga, In) were constructed to carry out comparative studies on the group III σ-hole interactions and π-hole interactions. The two types of interactions are all partial-covalent interactions; the π-hole interactions are stronger than σ-hole interactions. The electrostatic energy is the largest contribution for forming the σ-hole and π-hole interaction, the polarization energy is also an important factor to form the M···N interaction. The electrostatic energy contributions to the interaction energy of the σ-hole interactions are somewhat greater than those of the π-hole interactions. However, the polarization contributions for the π-hole interactions are somewhat greater than those for the σ-hole interactions.

The characteristics and nature of the halogen bonding in a series of BÁÁÁXY (B = H 2 S, H 2 CS, (CH 2 ) 2 S; XY = ClF, Cl 2 , BrF, BrCl, Br 2 ) complexes were analyzed by means of the quantum theory of ''atoms in molecules'' (QTAIM) and ''natural bond orbital'' (NBO) methodology at the second-order Møller-Plesset (MP2) level. Electrostatic potential, bond length, interaction energy, topological properties of the electron density, the dipole moment, and the charge transfer were investigated systematically. For the same electron donor, the interaction energies follows the BÁÁÁBrF [ BÁÁÁClF [ BÁÁÁBrCl [ BÁÁÁBr 2 [ BÁÁÁCl 2 [ BÁÁÁClBr order. For the same electron acceptor, the interaction energies increase in the sequence of H 2 S, H 2 CS, and (CH 2 ) 2 S. Topological analyses show these halogen bonding interactions belong to weak interactions with an electrostatic nature. It was found that the strength of the halogen-bonding interaction correlates well with the electrostatic potential associated with halogen atom and the amount of charge transfer from sulfides to dihalogen molecules, indicating that electrostatic interaction plays an important role in these halogen bonds. Charge transfer is also an important factor in the halogen bonds involved with dihalogen molecules.Keywords Halogen bond Á Topological analysis of electron density Á Natural bond orbital analysis Á Electrostatic interaction Á Charge transfer

The character of the cooperativity between the HOX···OH/SH halogen bond (XB) and the Y-H···(H)OX hydrogen bond (HB) in OH/SH···HOX···HY (X = Cl, Br; Y = F, Cl, Br) complexes has been investigated by means of second-order Møller-Plesset perturbation theory (MP2) calculations and "quantum theory of atoms in molecules" (QTAIM) studies. The geometries of the complexes have been determined from the most negative electrostatic potentials (V (S,min)) and the most positive electrostatic potentials (V (S,max)) on the electron density contours of the individual species. The greater the V (S,max) values of HY, the larger the interaction energies of halogen-bonded HOX···OH/SH in the termolecular complexes, indicating that the ability of cooperative effect of hydrogen bond on halogen bond are determined by V (S,max) of HY. The interaction energies, binding distances, infrared vibrational frequencies, and electron densities ρ at the BCPs of the hydrogen bonds and halogen bonds prove that there is positive cooperativity between these bonds. The potentiation of hydrogen bonds on halogen bonds is greater than that of halogen bonds on hydrogen bonds. QTAIM studies have shown that the halogen bonds and hydrogen bonds are closed-shell noncovalent interactions, and both have greater electrostatic character in the termolecular species compared with the bimolecular species.

The σ-hole interaction, which occurs between the covalent IV-VII atoms and nucleophilic substances, has become a hot issue of weak interaction. In this work, NCF···O=PX3···(NCF)n (X = F, Cl, Br, H, CH3·; n = 0, 1, 2) complexes were constructed and studied based on the second-order Møller-Plesset perturbation theory (MP2) calculations to investigate the enhancing effects of group V σ-hole interactions on the F···O halogen bond. With increasing n, the FO halogen bond becomes stronger, indicating that the group V σ-hole interactions could enhance the F···O halogen bond. As the capacity of donating electrons of X increases, the most negative electrostatic potentials outside the oxygen atom of O=PX3···(NCF)n (n = 0, 1, 2) become more negative, resulting in a stronger F···O halogen bond. In the formation of a F···O halogen bond, along the sequence of X = F, Cl, Br, H, CH3 of the negative sites O=PX3, the electric field of the lone pair of oxygen becomes greater and causes a larger decrease in electron density outside the fluorine atom. On the other hand, with increasing n from 0 to 2, the group V σ-hole interactions also increase the electric field of lone pair of oxygen and results in a larger decrease in electron density outside the fluorine atom.

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