RESULTS AND DISCUSSION
Geometrical structure parameters of studied systems
Figure 1 show in a schematic way investigated structures of modelled
complexes obtained using one of the presented above calculations
methods. All geometrical structures are of course linear. Each of the
systems and monomers achieved a minimum on the potential energy surface
during the optimization procedure what was confirmed by obtained
frequencies values. There were no imaginary frequencies designed in
Gaussian and Molpro as a negative value.
The most important structural parameters of this work are intermolecular
interaction distances as one of the main properties responsible for
complex stability and its reactivity. The calculated carbon-halogen
interaction distances values have been presented in Table 1. Four of six
studied here systems were also the subject of experimental
investigation. Those studies focused, first of all, on the spectroscopic
properties and charge contribution inside complexes appearing in their
gas phase. Obtained in experiments values of intermolecular distances
referring to the interesting systems have been also collected in Table
1.
The most predictable changes of the values showed here OC∙∙∙BrF and
OC∙∙∙ClF. In the first of them, the interaction distance is the shortest
in every used computational technique and basis set and in the second
place in this regard is OC∙∙∙ClF. The next is the
OC∙∙∙F2 and OC∙∙∙BrCl. Unfortunately, in the case of
OC∙∙∙F2 occur some disproportions. It can be seen on the
level ωB97X-D of theory where the C∙∙∙F distance is the longest among
all complexes and this result, including aug-cc-pVDZ basis set, is equal
3.407Å and for aug-cc-pVTZ 3.472 Å. It is ≅ 0.5 Å longer than the
optimized structure comes from the same exchange-correlation functional
without dispersion correction. M11 functional in a combination of
aug-cc-pVTZ has been given in the case of OC∙∙∙F2complex about 0.186 Å longer interaction distance than in OC∙∙∙BrCl. For
the double zeta basis set these discrepancies do not occur. If the last
two complexes (OC∙∙∙Br2, OC∙∙∙Cl2) will
be considered in the order of increasing interaction distances the
situation from a calculation point of view is not especially clear.
Experimental data distinctly indicate that carbon-halogen interaction is
longer about 0.082 Å in OC∙∙∙Cl2. Taking into account
the results obtained by using the aug-cc-pVDZ basis set the same quality
dependencies as in the experiment are preserved in case of using double
hybrid functionals (excluding B2GP-PLYP) (also with empirical dispersion
D2 and D3 corrections), B3LYP, ωB97X, and M11. Whereas the same results
for the aug-cc-pVTZ basis set reveal in addition that B2PLYP-D2 and
B2PLYP-D3 also do not keep the direction consistent with the experiment.
Summarizing the above, the following relationship may be written for the
C∙∙∙X distance from the shortest to the longest:
\(OC\bullet\bullet\bullet\text{BrF}<OC\bullet\bullet\bullet ClF<OC\bullet\bullet\bullet F_{2}\ \left(\text{except\ }\omega B97XD\ and\ M11\right)<\)
\(<OC\bullet\bullet\bullet BrCl<OC\bullet\bullet\bullet\text{Br}_{2}<OC\bullet\bullet\bullet\text{Cl}_{2}(depends\ on\ the\ method)\).
(4)
Intermolecular distance considerations, in relation to different
computational levels within each of the basis sets, have been shown
there is no simple correlation.
Table 2 illustrates the changes in bond length between halogen atoms
(X–Y) after complex creation. The values there are given (in angstroms)
as the result of the expression
\({\Delta}R_{XY}=R_{XY}^{\text{complex}}-R_{XY}^{\text{monomer}}\). (5)
The O≡C distance was not included in Table 2 because the biggest
difference of it between complex and monomer not exceeded ±0.004 Å.
Skipped also results for aug-cc-pVDZ. It was noted that the equation (5)
has been given practically the same values for both basis set. The
differences between aug-cc-pVDZ and aug-cc-pVTZ for the same complexes
and techniques were about ±0.004 Å for X–Y bond lengths and maximum
±0.001 Å in case of O≡C.
Analysis of the mentioned table draws attention to two things. Firstly
all the changes are positive. It means that all bonds have been slightly
elongated when the complexes were formed. The highest values are
observed for Br–F, whereas the lowest for F–F. As for used
calculations techniques, the most changes of halogen-halogen bond
lengths of investigated systems in relation to the isolated dihalogen
monomers are visible for B3LYP and its modification after adding
dispersion correction both of D2 and D3. For example,
RBr–F for these mentioned methods is equal
approximately 0.05 Å and for CCSD(T), MP2 and M11 0.015 Å, 0.022 Å and
0.012 Å respectively, what together with ωB97X (0.017 Å) gives the
smallest changes here. Such dependence repeats more or less for all
complexes.
At the end of this part, it should be stated that the largest
interacting distances C∙∙∙X usually correspond to those molecular
systems where the dipole moment values of electron donors are the
smallest. It is visible here in the case of the BrF group that shortens
halogen bond length the most and Br2 or
Cl2 act inversely. Interatomic distance is, therefore,
one of several parameters helpful in understanding the nature of XB.
Whereas for investigated model monomers the results collected in Table 2
are very small which leads to the conclusion that geometrical changes in
monomers groups are rather negligible and the investigated specific
interaction creation has no influence on the physicochemical properties
of O≡C and X–Y groups.
Interaction energy and its decomposition
It was already above mentioned that the LMOEDA procedure gives five
energy terms, where their sum is corresponding to the interaction
energy. The electrostatic component refers to the repulsion between
electrons and the attraction between electrons and atomic nucleus as
well as the nucleus-nucleus repulsion. In contrast to the SAPT, LMOEDA
treats exchange and repulsion energy contributions separately. In fact,
both energy types are strictly related to the Pauli exclusion principle.
Polarization energy change includes so-called orbital relaxation i.e.
orbital modifications during and after complex creation. The last term
is the London dispersion energy, which is always attractive and is
associated with electron correlation.
In this work, all interaction energies have been included BSSE
correction. All energy values coming from LMOEDA calculations are
collected in Table S1 in support information. This table has been also
enriched by interaction energies values designed as
ΔEint(opt). Letters „opt” mean that
ΔEint values do not come from LMOEDA procedure, but they
are obtained based on the optimized structures of complexes and monomers
and their total energies calculated in Gaussian and Molpro program
packages according to the formula (1) and (2). It is very important to
compare different methods and draw appropriate conclusions as to their
correctness.
In Figure 2 there are presented bare graphs that show interaction energy
components (in kcal/mol) for used here calculations techniques. The data
refer to the aug-cc-pVTZ basis set only because the results for
aug-cc-pVDZ and aug-cc-pVTZ are quite like each other especially in
terms of quality. The mentioned Table S1 includes both basis sets.
However, Figure 2 does not consider DFT methods with dispersion
correction. Exchange-correlation functionals with D2 and D3 have been
considered separately due to technical and computational reasons. In
every case, it was added for comparison (apart from individual component
energies) the values of total interaction energies,
ΔEint, obtained also from the decomposition energy
method. Bar plots illustrate also (yellow bar) the sum of exchange and
repulsion energy for every complex. Exchange energy is rather
stabilizing energy but repulsion energy on the contrary. These two
quantities act in opposite directions however they behave according to a
similar scheme. Hence it was decided to group them into a single term
called EX+REP.
From the first five graphs, (a)÷(e), (see Figure 2) some conclusions can
be drawn. First of all, it is that the biggest absolute energy values
occur always for the OC∙∙∙BrF complex independently from the used
calculation level. It refers to each individual energy type and to
interaction energy as well. Outstanding this system from others can be
explained through interatomic interaction distance analysis. As it
appears from the already discussed Table 1 the shortest XB is just for
OC∙∙∙BrF. The consequence of it should be the lowest value of
interaction energy. It was confirmed both for ΔEintobtained from LMOEDA and in the calculation of
ΔEint(opt). The next shortest C∙∙∙X distance is in
OC∙∙∙ClF. It was also reflected in mentioned energies values and in
total interaction energy. Graphs from (a) to (e) presented in Figure 2
confirm similar dependencies for systems in relation to different used
here methods although DFT functionals seem to have got tend to
overestimate components and interaction energies values. The biggest
energy scale scattering has been given B2PLYP and B3LYP techniques (from
about -40 to almost 100 [kcal/mol]).
Arousing the most doubts are here the calculations at the ωB97X and M11
level of theory. LMOEDA does not work especially well with these DFT
functionals. Final results in the interaction energies form seem to be
reliable but component energies are irrational. As indicated in Figure 2
and Table S1 the values of electrostatic (ES) and polarization (POL)
energies are huge. In addition, ES is positive. As it is shown in the
attached table even exchange energy for ωB97X is positive in the case of
OC∙∙∙Cl2 and OC∙∙∙F2. The conclusion
from this is some long-range separated functionals should be excluded
from energy decomposition computations of used here procedure.
The next question is how the Grimme’s dispersion correction does work
with implemented in GAMESS algorithms? The answer has been illustrated
by means of Figure 3 and Table 3. Figure 3 represents linear plots of
ΔEint and ΔEint(opt) (in kcal/mol)
values calculated for every six complexes in the aug-cc-pVTZ basis set.
The chart (a) refers to the double-hybrid B2PLYP-DN XC functionals,
where N=2, 3. Whereas B2PLYP (B2PLYP-DN str.) means that the geometrical
structure of complexes was optimized at the B2PLYP-DN level and LMOEDA
was carried out without proper dispersion correction. The symbol „opt”,
as earlier was described, includes interaction energy calculated
directly from Gaussian or Molpro (CCSD(T)) program packages but with
taking into account BSSE. The investigations omitted B2GP-PLYP-DN
functional because both in Gaussian and GAMESS dispersion is bad
implemented for it. As a result, it was obtained identical values for
B2PLYP-DN and B2GP-PLYP-DN. In turn, the charts (b) and (c) include
B3LYP and ωB97X respectively and their enriched about DN versions. In
Table 3 there are additionally collected ΔEint and
ΔEint(opt) values of complexes for B3LYP and B3LYP-D3
only, to better visualize the changes after the used of dispersion (for
both basis sets).
The analysis of Figure 3 should be noticing some similar relationships
for each of the three presented methods. Firstly, interaction energies
obtained by using pure functionals (without dispersion correction) both
in LMOEDA and in standard approach are very similar. The lines almost
overlap themselves. It is evidence that the results coming from three
different programs can be compared to each other and computations are
reliable. Secondly, energy decomposition procedure when dispersion was
not included in DFT functionals but the geometrical structures of
complexes were earlier optimized with added empirical dispersion
correction gives also very similar ΔEint values as in
case of the structures obtained without DN correction despite the small
differences in geometrical parameters of studied systems. For example,
curves B2PLYP, B2PLYP (B2PLYP-D2 str.), B2PLYP (B2PLYP-D2 str.)-opt,
(B2PLYP-D3 str.) and (B2PLYP-D3 str.)-opt are almost identical. On the
other hand, however performances of LMOEDA calculations taking into
account dispersion correction have been given completely different and
senseless values of interaction energies. It is especially visible for
B3LYP-DN and ωB97X-DN techniques. Table 3 shows that
ΔEint in relation to ΔEint-opt is not
only incomparable in any way but for OC∙∙∙Cl2 and
OC∙∙∙F2 is also positive (for B3LYP-D3). The presented
table in support information to this publication contains more such
irregularities. Moreover, Su et al .[56]unambiguously confirmed that the current LMOEDA version does not work
properly with functionals containing dispersion correction and the
functions corresponding for long-range description.
To better understand the meaning of each kind of component energy in
halogen bond creation of investigated systems Figure 4 was depicted. The
bar plots here contain energetic data in percentage terms in relation to
the concrete complex. The values, as in earlier figures, include the
aug-cc-pVTZ basis set only. It was inserted the results referring to the
following calculation methods: typical ab initio CCSD(T) and MP2
techniques, double hybrid B2PLYP functional and the most known hybrid
DFT functional i.e. B3LYP. As it was revealed above the ωB97X, M11 and
all dispersion enriched functionals had to be skipped.
As one can expect, the contributions of individual energies in the
charts indicate clearly that both CCSD(T) and MP2 results are quite
closed to each other especially in terms of quality. Electrostatics and
dispersion play here the most important role in the stabilizing of the
complexes structure, however in the case of OC∙∙∙F2 the
dispersion effects increase significantly in comparison to the
electrostatic forces. Whereas for OC∙∙∙BrF and OC∙∙∙ClF dispersion gets
lower for the benefit of polarization energy. An energy decomposition
result obtained by using density functional theory reveals a bit
different dependence. As it was showed on the (c) and (d) plots the main
factor responsible for the systems’ indestructibility is electrostatic
and polarization energies. In the case of calculations at the B2PLYP
level of theory, the dispersion and polarization contribution are almost
the same for OC∙∙∙F2, whereas electrostatic and
polarization energies are comparable in OC∙∙∙BrF and OC∙∙∙ClF
structures. Somewhat closer to the CCSD(T) and MP2 plots are the bars
presented in (d) diagram. From all negative values in
OC∙∙∙F2 the DISP is the most significant as in ab
initio and in the rest of the systems, the tendencies are similar. In
the end, it must be said that the greater halogen bond energy, the less
participation of dispersion energy in it and the bigger the meaning of
polarization.
QTAIM and ESP analysis
The last step of the research was to better understand the dependencies
governing the electron density and charge distribution in investigated
systems and their influence on the XB formation.
Quantum Theory Atom in Molecules (QTAIM) allowed finding and analysis
all critical points referring to the structure of each complex and
monomer. In this work, the main interesting objects are these
corresponding to create of bonds and intermolecular interaction. They
are so-called Bond Critical Points (BCPs) represented by saddle point
(3, -1) taking into account the direction of electron density changes.
The result data coming from calculations carried out in the AIMAll
program package had been revealed seven critical points, two of which
included bonds and one refers to intermolecular C∙∙∙X interaction.
Figure 5 illustrates the exemplary deployment of BCPs based on the
OC∙∙∙BrF structure. Coordinates of these points are almost the same in
the case of each complex. Notice the BCP corresponding O≡C bond is
displaced to the oxygen direction. The other two of these points are
rather located symmetrically.
Considerations have been included here following five parameters and the
relationships between each other: interatomic distances and bond
lengths; total interaction energies (ΔEint and
ΔEint-opt); electron density values (ρ(r)) and Laplacian
of the electron density (∇2ρ(r)). Similarly as in case
of decomposition energy significant part of results has been placed in
support information in table form designed as Table S2. This table
contains total interaction energies and Laplacian of the electron
density values for every used here calculation method in both basis
sets. It needs to be highlighted that the AIMAll program package does
not include triple excitations in the coupled-cluster method. Thus, it
was used CCSD technique for the structures optimized at CCSD(T) level of
theory. ∇2ρ(r) in the mentioned table refers to the
BCP localized between two monomers, O≡C and X–Y, that corresponds to
halogen bond. ∇2ρ(r) values play a significant role in
studies of the properties of chemical bonds because they specify where
the electron density is the most concentrated. This quantity is directly
related to potential energy (V(r)), and the density of kinetic energy
(G(r)). The equation connecting these parameters to each other can be
written as
\(\frac{\nabla^{2}(\rho)}{4}=2G\left(r\right)+V(r)\ \). (6) It
should be pay attention also for the sign of ∇2ρ(r).
The negative values of ∇2ρ(r) mean that V(r) is in
local excess. In the opposite situation, the charge is more depleted and
the G(r) is a dominant factor. As can be seen in the attached table all
results for Laplacian are positive. The papers[57,58] proves, that
∇2ρ(r)>0 occurs in the case of
closed-shell interactions.
Table 4 is enriched (except ΔEint and
∇2ρ(r)) with additional already mentioned parameters:
distances, ρ(r) and ∇ρ(r). It was focused here on a detailed analysis of
the results obtained at two calculation levels: CCSD and B3LYP.
Considerations of Table 4 reveals that the O≡C bond lengths and
topological parameters of BCP are very similar in every complex
calculated by using the same method and basis set. Density and Laplacian
values are here positive, and it is typical for covalent polar
bonds.[59] What is interesting, however, the
differences between basis sets are very significant especially for
∇2ρ(r). Notice that ∇2ρ(r) of O≡C is
more than two times higher in the case of aug-cc-pVDZ at the CCSD level
and over and above three times for the B3LYP method in comparison to
aug-cc-pVTZ results. Whereas the Laplacian values for the X–Y bond type
are very low, and they have various signs (positive or negative), that
suggests the different character of X–Y bond. For example, the shortest
distance here is in the case of F–F in OC∙∙∙F2 and the
∇2ρ(r) gives the highest numbers. However, generally,
there are no unambiguous dependences between bond lengths and Laplacian
values. The Cl–F bond length in OC∙∙∙ClF is the second shortest
distance of X–Y among all studied systems but for presented two
calculations methods in the aug-cc-pVTZ basis set have the lowest
(negative) values of ∇2ρ(r). This may suggest more
shared shell interaction what practically means the stronger covalent
bond character. It is worth to pay attention that in the case of a
halogen-halogen bond, there occur a bit more disproportionate
differences in values and signs of Laplacian (depending on the adopted
computational method and basis set) than for O≡C bond and halogen bond.
Halogen bond geometrical, energetic and topological parameters were
presented not only in Table 4 and in the enclosed Table S2, but the data
was also depictured in Figures 6-8. Figure 6 contains four plots
illustrating interaction energy, halogen bond length, electron density
and Laplacian as a function of complex type. It can be seen immediately
some dependencies between proper curves. Plots (c) and (d) have almost
identical shapes with this exception, that in the case of
∇2ρ(r), the values are about two times higher than for
ρ(r). In turn, on the plots (a) and (b) the most significant differences
are noticeable for the OC∙∙∙F2 system, where for the
weakest interaction the range of XB is shorter than for stronger halogen
bonds in OC∙∙∙Br2, OC∙∙∙Cl2 and in
OC∙∙∙BrCl. It is also visible, that the B3LYP technique had been given
less dispersion of results between used basis sets, particularly for the
cases of OC∙∙∙BrF and OC∙∙∙ClF systems presented on the plots (a)÷(c).
Summarizing Figure 6, with the assumption of omission of
OC∙∙∙F2 complex, the general tendency is that the
shorter XB the greater the value of electron density and Laplacian. It
seems the correlations between halogen bond power and structural or
topological parameters should be easier to find because investigated
systems have the same Lewis base and different Lewis acids. Plots in
Figure 7 indicate to a lesser or greater extent on certain dependencies.
Plot (a) illustrates ΔEint=f(RC∙∙∙X) and
the slope of the straight lines is positive in comparison to other plots
that are coincident with information from the previous figure.
Nevertheless, the correlation coefficients especially these referring to
the CCSD level are very low (R2≅0.32 or
R2≅0.54). The situation on the plot (b) looks a little
better. Laplacian values in relation to the XB length had been given
determinant coefficients equal to R2≅0.64 or
R2≅0.79 for CCSD/aug-cc-pVDZ and CCSD/aug-cc-pVTZ
respectively. In the case of the DFT method, the fitting is very well
(R2>9). Much better functions for the
description of XB strength can be obtained by the replacement
RC∙∙∙X by ρ(r) or by ∇2ρ(r) and it was
presented on the plots (c) and (d) in Figure 7. The linear dependence of
interaction energy relative to one of the mentioned topological
parameters is here greater than 0.9. Hence the conclusion is that the
parameters obtained by using QTAIM methodology give much more
predictable results in studies of XB strength than in the case of
traditional geometrical data.
The molecular electrostatic potential distribution has been shown in the
form of electrostatic potential plot in Figure 8 and was generated for
the three monomers (OC, Br2, ClF) and two complexes
(OC∙∙∙ Br2 and OC∙∙∙ClF). Presented MEP calculations
were carried out at the B3LYP/aug-cc-pVTZ level of theory. From the
pictures can be concluded that the σ-hole is observed for Br–Br and
Cl–F, but in the first case, the positive charge is at the cusp point
from both sides (on every Br atom). Whereas the second monomer has a
positive charge, that is focused at the peak of the chlorine atom. The
most intensive blue colour means the most positive charge with the
values of about 0.03 a.u. It is also clear that the electron-rich area
on the carbon and oxygen atom can be a very good candidate for the
creation of directional interaction. The pictures (c) and (d) refer to
the formed complexes where changes of MEP are not drastic in comparison
to monomers.
CONCLUSIONS
The main aim of this paper was to analysis six complexes with linear
interaction through halogen bond from the point of view of their
interaction energy and influences this energy and every one of its
components for the halogen bond formation and strength. Investigated
complexes are not only theoretical systems but they are also synthesized
fully, and they were an object of few experimental studies.
In the first place, it was tried to find the dependencies between the
lengths of proper bonds before and after XB creation. As was shown the
changes for O≡C were negligibly small. Also, in the case of XY, the bond
length changes between monomers and complexes were very small although
all XY bonds lengthened itself after the creation of complexes, what was
the most visible for the B3LYP method. In addition, there were no
significant differences between used basis sets. In turn, for
carbon-halogen interaction distance, finding more precise correlations
was not so easy. The shorter XB was noted for the OC∙∙∙BrF complex and
then for the OC∙∙∙ClF in every used computational technique. Other
systems have less predictable dependencies much closer related to the
adopted method of studies.
LMOEDA generally had been given reliable results except for two things.
Firstly, the using ωB97X and M11 leads to irrational enormous values of
electrostatics and polarization energies and the second thing is
completely bad working this procedure with exchange-correlation
functionals enriched of Grimme’s dispersion corrections, and
particularly with B3LYP-DN and ωB97X-D, where the total interaction
energy values for the OC∙∙∙F2 was unfortunately positive
(in the case of B3LYP-D3 it was observed positive energy for
OC∙∙∙Cl2 as well). Additionally, B2GP-PLYP is in the
opinion of authors bad implemented in Gaussian as well as in LMOEDA
algorithms in GAMESS because the results were identical as in the case
of B2PLYP, both at geometrical properties level obtained in the
optimization process and for energy decomposition. The component energy
playing the main role in the stabilizing of the complexes structure was
different and depending on the method. Generally, it can be said that
for ab-initio techniques they were electrostatics and dispersion
energies. Whereas in the case of DFT theory dispersion decreased in
relation to the polarization energy.
QTAIM theory was used for finding and description of bond critical
points (3, -1) in investigated modelled complexes. For every system are
three such points. Two of them correspond to the covalent bonds between
atoms in monomers parts and the third is localized between C and X atom
and refers to noncovalent interaction, this is halogen bond. The
analysis of the results indicates that for this BCPs the values of ρ(r)
and ∇2ρ(r) are all positive what means that G(r) in
equation (6) plays a dominant role. It is visible to closed-shell
interaction. It should be noted here that the topological parameters are
better for comparison of the strength of halogen bonds because
dependences of interaction energies in relation to one of the mentioned
above parameters are more linear.
In the end, molecular electrostatic potential confirmed the creation of
a positive charge region on halogen atoms called the σ-hole and on the
other hand the accumulation of negative charge on carbon and oxygen
atom. As it is commonly known plus and minus charge can form attractive
forces between each other what leads to the stabilization of such
complexes as presented here.
ACKNOWLEDGMENTS
The authors are grateful to the Wroclaw Centre for Networking and
Supercomputing for a generous allocation of computer time.
CONFLICTS OF INTEREST
Authors declare no conflicts.
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LIST OF FIGURES
Figure 1. Schematic presentation of model systems including
intermolecular halogen bonding constituting the subject of the studies.
Figure 2. Contributions of individual energy components in
total interaction energy as LMOEDA result. ΔEint was
also presented on charts for comparison. The charts included
calculations carried out in the aug-cc-pvTZ basis set.
Figure 3. Plots illustrating differences in
ΔEint for used exchange-correlation functionals, with
and without empirical dispersion correction of Grimme. The data include
each complex (aug-cc-pVTZ basis set). The three charts present results
obtained at the (a) B2PLYP, (b) B3LYP and (c) ωB97X level of theory
respectively, as the basic XC functionals.
Figure 4. Stacked bars plot of percentages shares of component
energies including four selected methods: (a) CCSD(T)/aug-cc-pVTZ, (b)
MP2/aug-cc-pVTZ, (c) B2PLYP/aug-cc-pVTZ and (d) B3LYP/aug-cc-pVTZ.
Figure 5. One of the complex structures o(OC∙∙∙BrF) as an
example of critical bonding points (3, -1) deployment. Results obtained
in the AIMAll program package at the MP2 level of theory using the
aug-cc-pVDZ basis set.
Figure 6. Plots showing (a) ΔEint[kcal/mol], (b) C∙∙∙X interaction distance [Å], (c) electron
density [a.u.], (d) Laplacian of density [a.u.] for every
complex type. It has been selected two computational methods for
comparison: CCSD and B3LYP in both basis sets. All data here refers to
the intermolecular BCP.
Figure 7. Correlations between interaction energies and (a) XB
binding distances, (c) electron density, (d) Laplacian of density.
Whereas the second plot (b) indicates Laplacian of density as a function
of XB distance.
Figure 8. Exemplary electrostatic potential mapped on the
surface of molecular electron density at the B3LYP/aug-cc-pVTZ level of
theory for (a) OC, (b) Br2 and ClF, (c)
OC∙∙∙Br2, (d) OC∙∙∙ClF.