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].