INTRODUCTION
The specific noncovalent intra- and intermolecular interactions as the hydrogen bond (HB), the charge transfer (CT) and the halogen bond designed also as XB in literature are today one of the main subjects of interests both of experimental and theoretical chemistry. There is nothing surprising in this, taking into account the fact that their role in general creating of matter, in the functioning of biological structures, and also usability in many current chemical technologies and nanotechnology is crucial.
The interaction through a halogen bond was the first time described in the nineteen century[1] but opposite to the hydrogen bond was very rarely mentioned in scientific papers. The main problem was with the interpretation of its formation mechanism and stability. The basic question was why negatively charged halogen atom can interact with electron-rich Lewis base? Only the sudden development of experimental and theoretical methods in chemistry and physics allowed shaping the different concepts that help today to understand much better many properties and meanings of XB in nature.
Actually, common theory answering the above question mostly was proposed by Politzer, Murray, and Clark.[2,3] It is so-called the σ-hole theory. This theoretical approach connects XB formation with the polarization of halogens in the molecule, its influence to charge distribution and finally determines the properties of the system. As the name itself already indicates the fundamental thing is here the σ-bond between atoms. Considering a simple exemplary D–X∙∙∙Y scheme, where X is a halogen atom, Y is an electron-rich Lewis base (for example elements from 15 and 16 group of the periodic system and also anions of 17 group as F-, Cl-, Br-, I-)[4] or π-electrons. Whereas D may have got range from atoms like H, C, N, P and O to large inorganic or organic chemical groups containing very often heteroatoms and sometimes in a special case it may be also halogen atoms or groups.[5] Each of the halogens has on the valence shell seven electrons of which five of them on the p-orbitals. The most important (according to molecular orbital theory) electron that is necessary for σ-bond creation is located on pz orbital. Formation of the single bond leads in these situations to the depopulation of pz orbital, which is in the same line as the σ-bond. In this place, there is a region with electron deficiency designed as σ-hole. In other words, this positive charge on the X atom in a D–X monomer and the negative charge of Y interact electrostatically each other. This proposition of explanation of XB stability overthrows of the traditional way of reasoning, in which electron density is evenly distributed on X-atom.[6,7] The correctness of the σ-hole theory assumptions seem to be confirmed molecular electrostatic potential calculations (MEP).[8,9] In our own investigations, the MEP method also reveals a positive charge area in systems of X(1)-X(2) where both X are different halogen atoms connected by a single covalent bond. It will be more detailed discussed in the next parts of this paper.
An explanation based on this electrostatic approach has, unfortunately, like any theory, some weaknesses. Many theoretical methods give results dependent on adopted calculation models. Relative dispersion contribution is also discussed as well as concepts of charge transfer to these interactions types.[10]
The interaction energy is the main factor responsible for the build-up of supramolecular structures. In accordance with the postulates of quantum mechanics, the energy itself is observable. Referring to the chemical systems is the value of energy strictly related to atoms’ positions and dependent on the electronic state of the complex. The most important thing is that the interaction energy can be minimized by its division into multiple terms. Such an approach focuses, in particular, on the individual components of interaction energy which the description from a physical point of view is less complicated.
Therefore, in this paper, it has been focused on the theoretical study of halogen bond not only from the MEP point of view but first of all from the perspective of an energy decomposition analysis and chemical quantum topology. The work in which energy partitioning was taken into account the first time is probably presented by London.[11] The two most important modern calculation techniques are SAPT (Symmetry-Adapted Perturbation Theory)[12] and LMOEDA (Localized Molecular Orbital Energy Decomposition Analysis).[13] LMOEDA has been conceived to solving many difficult chemical systems because it can be used in closed- and opened-shell complexes. Moreover, it includes many computational levels and takes into account the correction of the basis set superposition error. This procedure is today more and more widely used because of its not complicated to carry out and due to the easy accessibility to the software.[14-18] For these reasons, it was decided in this work to use LMOEDA as a tool for interaction energy decomposition. Quantum topological parameters of critical points each of the structures of monomers and complexes were studied using Quantum Theory of Atom in Molecules (QTAIM) methodology.[19]
From a chemical point of view in the area of interest was simple model complexes with pronounced interaction through halogen bonding. It was decided to take for research six four-atomic and closed-shell complexes about linear structure. Their general structure can be writing as O≡C∙∙∙X–Y, where X and Y are F, Cl, Br atoms arranged in the following order (X, Y)=F; (X, Y)=Cl; (X, Y)=Br; X=Br, Y=F; X=Br, Y=Cl; X=Cl, Y=F. Iodine atom was omitted due to the necessity to take into account effective core potentials (ECP) in calculations. Most of these complexes and monomers structures have been investigated experimentally (especially in spectroscopic terms) and some properties of them were also calculated using ab initiotechniques.[20-26]
COMPUTATIONAL DETAILS
The whole project involved several stages of research: geometrical structures optimization of monomers and complexes, decomposition analysis of interaction energy in complexes, quantum topological studies every system and its component parts. All modelled systems have been investigated in a simulated gas phase state in a vacuum.
As for the geometrical structure optimization, the studies included several computational levels in Gaussian 16[27]and Molpro 2012.12.01[28] program packages (Molpro for coupled-cluster only). Among typical ab initio methods were used CCSD(T)[29-33] and MP2[34]. Whereas computations based on density functional theory (DFT) referred to the following exchange-correlation (XC) functional: B2GP-PLYP[35], B2PLYP[36], B3LYP[37,38], ωB97X[39] and M11[40]. Additionally, it was used also the dispersion correction of D2 and D3 developed by Grimme[41,42] for all of these functional except B2GP-PLYP (double hybrid functional) due to some technical troubles and except ωB97X where it was decided to the application only D2 correction implemented in ωB97X-D[43] XC functional. In turn, when it comes to basis sets have been applied aug-cc-pVDZ and aug-cc-pVTZ[44-46] in this work.
The interaction energy value each of the complex, ΔEint, was generally obtained from the expression
\({\Delta}{E}_{\text{int}}=E_{\text{complex}}-\left(E_{\text{OC}}+E_{\text{XY}}\right),\)(1)
where EOC and EXY are the total energies of monomers. It should be also noticed here that the basis set superposition errors (BSSE) in the case of systems optimization was removed in the procedure of the counterpoise method proposed by Boys and Bernardi[47]. Therefore the equation corrected energy can be written as the sum of equation (1) and mentioned amendment.
\({\Delta}{E}_{\text{int}}^{\text{CP}}={\Delta}{E}_{\text{int}}+\delta_{OC\bullet\bullet\bullet XY}^{\text{BSSE}}\)(2)
LMOEDA calculations were carried out using the GAMESS program package in version 2017.04.20-R1.[48] As a result of this decomposition procedure, the total interaction energy has been obtained as the sum
\({\Delta}{\ E}_{\text{int}}=E_{\text{ES}}+E_{\text{EXC}}+E_{\text{REP}}+E_{\text{POL}}+E_{\text{DISP}}\)(3)
in which every component means electrostatic, exchange, repulsion, polarization and dispersion energy respectively. Electrostatic, polarization and dispersion energies are attractive, whereas the sum of the exchange and repulsion are repulsive.
QTAIM investigations have been especially focused on the analysis of Laplacian (∇2ρ(r)) of the electron charge density ρ(r), that refers to the (3, -1) critical points corresponding to bonds. All necessary here computations were performed using AIMAll 17.11.14 B program package.[49]
Electrostatic potentials were studied also in Gaussian 16 including cube files generation indispensable to the mapped of MEPs on the electron density surfaces.
The graphical part of this work was made in two programs: Chemcraft 1.8[50] and Gaussview 6[51].