π‑Hole Halogen Bonds Are Sister Interactions to σ‑Hole Halogen
Bonds
Pradeep R. Varadwaj,* Helder M. Marques, Arpita Varadwaj, and Koichi Yamashita

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ABSTRACT: Halogen’s σ-hole interactions are found throughout the chemical, biological, and
crystal engineering literature. These interactions are directional and may be of van der Waals type,
weak, strong, or even very strong, with binding energies ranging between −0.01 and −100 kcal
mol−1. When occurring between interacting neutral molecular entities, the energy range is often
between −0.01 and −8.0 kcal mol−1. This study was undertaken to show there is crystallographic
evidence that a covalently bonded halogen in a molecule can present with p/π-holes that are
capable of engaging in attractive interactions with nucleophiles on an identical, or dissimilar,
neighboring molecule, and that the strength of the interaction between the p/π-hole halogen
bonded dimers can vary between −4.0 and −12.0 kcal mol−1 depending on the mode of that
interaction and whether other interactions are involved. To this end, density functional theory at
the M06 level with and without the effect of dispersion, in conjunction with the aug-cc-pVTZ
(aug-cc-pVTZ-PP for iodine) basis set, suggested for the study of halogen bonding, was
employed. Various charge density-based models were applied and the results of bonding modes
are elucidated. Analysis of molecular electrostatic surface potentials revealed the electrophilicity of the σ- and p/π-holes on the
surfaces of covalently bonded halogens in molecules, which were useful indicators for the formation of σ- and p/π-holes halogen
bonding interactions in the dimers studied. Individual interactions identified may be weak, but since they are collective, they
strengthen the geometry of the dimers formed. Furthermore, periodic calculations of two crystalline systems (CF3ICl2 and CF3IClF)
reveal that they are direct bandgap materials, indicating the importance of halogen bonding in the design and subsequent growth of
such materials for application in optoelectronics.

1. INTRODUCTION
Crystal growth and design is an important aspect of the
engineering of chemical systems,1−5 which is an active field in
the broad area of materials nanoscience and technology.6 It
deals with the study of crystals as chemical systems, their
geometry, shape and physical properties in both amorphous
and crystalline forms. Molecular entities (viz. neutral molecules
and ions in molecular and/or atomic forms) are their building
blocks, which are self-assembled by a variety of intermolecular
forces. The forces are adhesive in nature, and when properly
engineered between atomic/molecular basins, result in
ordered, functional materials. They are widely recognized as
intra- or intermolecular interactions and are key chemical
synthons that appear largely as σ-,7,8 p-9,10 and/or π-hole
interactions.11−14

σ- or π-holes in molecules are generally understood to be
electron density deficient (electrophilic) regions on covalently
bonded atoms in a molecule, but they can be electron density
rich as well. When the former, they are capable of donating σ-
or π-holes as electrophiles, and when the latter, they can be
regarded as electron density donors (for example, the negative
σ-hole on F in the HF molecule15).
A σ-hole appears on the opposite side of the R−A bond

extension of the covalently bonded atom A, whereas a p/π-hole

appears on the surface of atom A perpendicular to the R−A
bond axis, or in the junction region between close-lying
unbound atoms, or around the bond region, or in the plane of
the molecule; R is the remainder part of the molecule. For
example, the σ-hole is electrophilic on the side of atom X
opposite the X−X bond in a dihalogen molecule X2 (X = F, Cl,
Br, I), and nucleophilic on the side of F opposite the C−F
bond in CH3F and HF. Similarly, an electrophilic p/π-hole can
be observed on the surface of N in substituted NO2,

16 and in
PnX3 molecules (Pn = P, As, Sb, Bi),17−19 around the N�N
triple bond in N2,

20 in the junction region in between a pair of
two neighboring C−F bonds and on the centroid portion of
the C6 ring in in C6F6. Bauza ́ and co-workers have shown that
nitromethane and nitrobenzene are able to interact favorably
with electron-rich molecules by means of the p/π-hole that is
located above and below the C−N bond.16 Similarly, B in BF3

Received: March 30, 2024
Revised: August 25, 2024
Accepted: August 26, 2024
Published: September 9, 2024

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https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Pradeep+R.+Varadwaj"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdf
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is widely known to have a pair of π-holes on its outer surface
orthogonal to the plane of the molecule, yet Tarannam et al.9

and Taylor10 passionately asserted that the designation “p-
hole” is far more apt, as the existence of an empty p-orbital
embodies a concept that is profoundly distinct from the origin
of a π-hole.
A nucleophilic p/π-hole (or p/π-belt) can be observed on

many arene moieties, as well as around the C�C triple bond
in acetylene and on the planar centroid portion of the C6 ring
in C6H6. These and perusal of the noncovalent chemistry
literature clearly suggest that the electrophilic and nucleophilic
strengths of these “holes”, or “belts”, depend on many factors,
including the type of atom(s), the periodic table group to
which it (they) belongs, its (their) electronegativity, polar-
izability, and the nature of the electron-withdrawing group R to
which it (they) is covalently bonded. Since either of these (p
or π) holes/belts emerge from a p-type orbital (or even p-type
Rydberg valence orbitals) orthogonal to the covalent bond axis
in a molecular entity, we, hereafter, refer to them as p/π-hole
(or p/π-belt).
Typical binding energies for many dimer systems involving

σ-hole interactions in neutral molecules have been reported to
range from −0.01 to −8.0 kcal mol−1.21−28 If the σ-hole on
atom A in the R−A molecule is stronger and the remainder R
is very polarizable, the binding energies of the resulting
complexes will be larger. Indeed, if an anion binds to the σ-
hole of a neutral molecule, the strength of the interaction may
exceed the so-called covalent bonding limit of −40.0 kcal
mol−1.1,29,30 The ion-pair adduct formed by the involvement of
the σ-hole on the cation is characterized by very large
interaction energies,31,32 and a significant portion of this
energy arises from point−charge interactions driven by
Coulombic forces. This concept may also be applicable to
the energies of p/π-hole (or p/π-belt) interactions in
complexes.
Electrophilic π-holes have been visualized experimentally

using Kelvin probe force microscopy.33 They have also been
reported on the electrostatic surface of elements of groups 14,
15, 16 and 18. When belong to these particular groups, they
can be referred to as a π-hole tetrel bond,34 pnictogen
bond,35,36 chalcogen bond,37 and aerogen bond,38 respectively.
The π-hole bond donating proficiency exhibited by groups 14
and 18 are not rare, but that due to a halogen derivative (group
17) in molecules is very rare,14,38,39 although halogen can be
involved in counterintuitive interactions has been demon-
strated by Murray and Politzer.26 Zierkiewicz et al.14 have
speculated that halogen atoms in molecular entities may host a
π-hole in hypervalent bonding situations. This was exemplified
by showing that a crystal formed from the BrOF2

+ cation was
stabilized in the presence of two KrF2 and one AsF6

− anion
moiety as building blocks. Although the Lewis bases in the
latter three molecules appear to interact through a σ-hole on
the covalently bonded Br atom in BrOF2

+, it was suggested
that the existence of a π-hole site on the BrOF2

+ cation, which
has the strength to attract another Lewis base, cannot be ruled
out, a result similar to that found by one of us in a recent
study.40

We have recently revisited the definition of the halogen
bond (HaB) (IUPAC recommendations 201341)42 and have
put forward an ambitious revision inspired by a multitude of
groundbreaking studies employing cutting-edge computational
and experimental techniques. Our proposed updates encom-
pass an extensive array of detailed annotations and distinctive

features, supplemented by a rich tapestry of examples
showcasing various donors and acceptors engaged in HaB
formation. We have also curated a selection of illustrative
crystal systems that vividly demonstrate the nuances of halogen
bonding, including the intriguing possibility of interactions
involving p/π-holes or p/π-belts.
Although the views given in ref 14 concerning p/π-holes and

their involvement in halogen bonding may be speculative, it
would be interesting to verify whether hypervalent halogen
derivatives in molecules other than cations generally exhibit p/
π-holes and whether they can form p/π-hole HaBs with the
nucleophiles with which they interact. If so, what is the
strength of the interaction that determines the stability of the
complexes so formed? What are the current state-of-the-art
theoretical methods for revealing this? Do they follow the
guidelines and recommendations of the IUPAC working
group41 for identifying halogen bonding in molecules, crystals,
and crystalline systems? To this end, we have surveyed the
Cambridge Structural Database (CSD)43−45 and Inorganic
Crystal Structure Database (ICSD)46−48 and identified several
crystal systems to address these fundamental questions.
We undertook an extensive exploration using density

functional theory (DFT) calculations on a selection of dimers
in the gas phase, chosen from specific crystalline systems. Our
analysis delved into various descriptors to elucidate the nature
of halogen’s p/π-hole capability for forming noncovalent
bonds, employing three sophisticated theoretical frameworks:
molecular electrostatic surface potential (MESP),49,50 quantum
theory of atoms in molecules (QTAIM),51,52 and independent
gradient model (IGM).53−55 A central aim of this endeavor
was to ascertain whether the findings from the first model align
seamlessly with those derived from the subsequent two
models. To advance our investigation, we conducted precise
halogen substitutions on the parent molecules, fabricating an
array of model dimers to computationally uncover chemical
systems that may be useful for future synthetic endeavors. As
we bring our study to a conclusion, we provide a succinct
overview of the periodic calculations performed on two
experimentally known crystal systems, with a focus on their
bandgap properties. The insights garnered may pave the way
for innovations in materials design and discovery, particularly
through the intriguing phenomena of σ- and p/π-hole halogen
bonding.

2. CRYSTAL AND MOLECULAR SYSTEMS AND
COMPUTATIONAL DETAILS

CF3IF2, CF3ICl2, and CF3IClF are members of the
(trifluoromethyl)iodine dihalide, F3C−I-X2 (X = halogen),
family. Crystals of trifluoromethyl iodine difluoride (CF3IF2)
(ICSD ref 408935),56 and (dichloro-trifluoromethyl)iodine
(also called (trifluoromethyl)iodine dichloride (CF3ICl2))
(CSD ref COXYIX),57 have been known since 1998 and
1999, respectively, yet their materials properties (viz. bandgap
features) have not been explored to date. The crystal of chloro-
fluoro-(trifluoromethyl)iodine (CF3IClF) was reported in
2001 (CSD ref WOWYUC).58 Both CF3ICl2 and CF3IClF
crystalize in the orthorhombic space group Cmca, but CF3IF2
(ICSD ref 408935) crystalizes in the I42d space group. The
molecular form of each of them, as a building block, features a
T-shape structure, and this is taken into account in this study.
All geometric and energy stability calculations for the dimers

were performed using Gaussian 16,59 including geometric
optimization and subsequent frequency calculations. The latter

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resulted in positive eigenvalues of the Hessian (second
derivatives) of the energy with respect to the atom fixed
nuclear coordinates, confirming that the geometries of the
dimers reported in this study are a true stationary point at the
applied M0660 level of theory. The use of the DFT-M06
functional was based on its appreciable performance to
describe halogen bonded systems compared to other DFT
functionals and MP2, as reported in a recent benchmark
study.61 The aug-cc-PVTZ basis set was used for all atoms
except iodine, for which the pseudopotential basis set, aug-cc-
PVTZ-PP, obtained from the EMSL basis set library62−64 was
used.
The electrophilic and nucleophilic nature of various regions

on the surfaces of atoms in the monomer molecules were
examined using the MESP model,49,50 based on the electro-
static potential, V(r). Murray and Politzer.65,66 have already
demonstrated the usefulness of the model and the underlying
theoretical details several times, showing how suitable is the
physical observable, V(r), in describing the origin of non-
covalent interactions formed by chemical systems comprised
largely of main group elements of the periodic table. When an
appropriate isoelectronic density envelope of the molecule
under investigation is used on which to compute the potential,
two descriptors emanate from the MESP model. They are the
local most minimum and maximum of potential (VS,min and
VS,max, respectively). Their positive and negative signs are the
determinants of surface electrophilicity and nucleophilicity,
respectively, and their magnitudes are the determinants of their
strengths. The VS,max and VS,min are often (but not always!)
seen on the side of atom A along and around the covalent
bond extension in R−A, respectively.
QTAIM51,52,67−69 produces a molecular graph, composed of

bond path and bond critical point topologies of the charge
density, a theoretical approach that has been extensively
applied to molecular and intermolecular systems to provide
insight into the nature of the chemical bonding between
bonded atomic basins based on its unique space partitioning
approach that relies on the zero-flux boundary condition.
There are many descriptors of the model, but three crucial
descriptors are the charge density (ρb), the Laplacian of the
charge density (∇2ρb), and the total energy density (Hb). The
evolution of these properties rely on the existence of a bond
critical point between interacting atomic basins; failure of the
model to do so may mislead in identifying the presence of an
attractive interaction.70−73 On the other hand, the IGM
model53−55 has been demonstrated to reveal both intra- and
intermolecular interactions in and between the interacting
molecules via two its descriptors, IGM-δgintra and IGM-δginter.
They are represented by colored isosurface domains in low
density regions between noncovalently bonded atomic
moieties computed using low isovalues (typically around
0.01 au). The isosurfaces generated using the model are
generally colored red, blue, cyan, and/or green; the former
represents repulsion and the latter three represent attraction
depending on the decreasing nature of their energy strengths.
AIMAll,74 Multiwfn75 and VMD76 software were used.
The uncorrected and BSSE-corrected interaction energies of

the dimers were computed using eqs 1 and 2, where BSSE
refers to the basis set superposition error accounted for by the
counterpoise procedure of Boys and Bernardi,77 and ET refers
to the total electronic energy of individual species.

=E E E(dimer) (dimer) (sum of monomers)T T (1)

= +E E E(BSSE) (dimer) (BSSE) (2)

The effect of dispersion was considered at the level of
Grimme’s DFT-D3 (hereafter GD3) that accounts for the
original D3 damping function.78 The dispersion-incorporated
uncorrected and BSSE-corrected interaction energies are
referred as ΔE(GD3) and ΔE(GD3-BSSE), respectively.
Crystals of CF3ICl2 (CSD ref COXYIX),57 and (CF3IClF)

(CSD ref WOWYUC)58 were also examined using periodic
boundary conditions at the Perdew−Burke−Ernzerhof
(PBE)79 level of theory. The Vienna Ab Initio Simulation
Package (VASP 5.3)80−84 was used. The pseudopotentials
invoked emerged from the projector-augmented-wave (PAW)
method.85,86 The cutoff criterion for force on ions, energy for
plane-waves, and self-consistent loops were 0.01 eV Å−1, 520
eV and 10−6 eV, respectively. A k-mesh of 6 × 6 × 4 was used
to sample the Brillouin zone. Since there were no metals
involved, nonspin polarized calculations were performed. The
electronic band structures and density of states (DOS) were
plotted using the Sumo87 and pyband88 codes, respectively.

3. RESULTS AND DISCUSSION
3.1. Crystal Geometries and DFT Calculations.

3.1.1. (Trifluoromethyl)Iodine Dichloride (CF3ICL2) CRYSTAL.
Our analysis of the geometry of the CF3ICl2 crystal revealed
some close intermolecular contacts between the CF3ICl2
molecular building blocks as shown in Figure 1a. The key
chemical synthon that holds the CF3ICl2 molecules together is
the I···Cl contact. They are either shorter, or even longer, than
the sum of the van der Waals (vdW) radii of atomic I and Cl,
3.86 Å (rvdW (I) = 2.04 Å and rvdW (Cl) = 1.82 Å89). Some of
them are consistent with IUPAC’s distance-based feature,41

while others are not. This means that the recommended
IUPAC feature fails to fully identify and characterize HaBs.
However, as we34,35 and others90,91 have suggested before, and
which also appeared in our recently proposed relook at the
definition of the HaB (feature d),42 the reported vdW radii of
atoms of the periodic table may be accurate within an error of
±0.20 Å. Taking this into account, both the I···Cl close
contacts shown in Figure 1a could be regarded as HaBs.
The covalently bonded I atom in each CF3ICl2 building

block is noncovalently bonded to the six nearest Cl atoms of
six other identical molecules, forming six I···Cl close contacts
(Figure 1a). Four of these are p/π-hole HaBs and the
remaining two are σ-hole HaBs. The σ-hole HaBs are
quasilinear, with ∠C−I···Cl = 162.2° (and 148.0°) and r(I···
Cl) = 3.324 (and 4.345) Å. The latter contact is substantially
longer than the vdW radii sum of I and Cl [rvdW (I) + rvdW (Cl)
= 3.86 Å]. Similarly, a pair of p/π-hole HaBs occur on one side
of the C−I covalent bond axis and is 3.926 Å, while the other
pair appears on the other side with a length of 3.838 Å; the
former violates the IUPAC’s geometric feature for a HaB.41 All
four of these close contacts are directional and nonlinear. The
directionality arises from the Coulombic nature of these
interactions, i.e., positive sites interact with negative sites,
although the importance of exchange repulsion cannot be
discounted. The sum of the six noncovalent bonds and three
covalent bonds results in a pseudo-9-coordinate iodine in
CF3ICl2. This scenario may be reminiscent of the pressure-
induced formation of the neutral fluoride compound IF8,
composed of 8-coordinate iodine, that was recently reported
by Luo and co-workers.92 Similar chemical environments of
iodine in molecular entities have been reported by others,93,94

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for example, highlighting the occurrence of 9- and 12-
coordinate iodine.
The plot of the molecular electrostatic potential surface of

the CF3ICl2 monomer, Figure 1b, reinforces the view
developed above. As can be seen, the outer surface of the
covalently bonded I in CF3ICl2 is completely electrophilic
along and around the outermost extension of the (F3)C−I
bond. The σ-hole resides on the side of I along the outer
portion opposite to the C−I covalent bond, characteristic of
VS,max > 0 (VS,max = 45.0 kcal mol−1). Similarly, there are two
regions on the outer surface of I, each characterized by VS,min >
0 (VS,min = 16.5 kcal mol−1); they lie above and below the
plane formed by the Cl2IC fragment of the molecule, and that
are orthogonal to the C−I covalent bond. Each of these two
electrophilic regions are what we call iodine’s p/π-hole, and
originate from a p-type valence accepting orbital. It is worth
noting that electrophilic σ- and p-/π-holes on bonded atomic
surfaces in molecular entities are typically characterized by
VS,max > 0. The electron-density deficient electrophilic regions
on the iodine atom in CF3ICl2 are characterized by VS,min > 0,
but since they are orthogonal to the C−I bond axis, we refer to
them here as the p/π-holes. It is this p/π-hole in the CF3ICl2
molecule that is attractively engaged with the negative lateral

part of a pair of covalently bonded Cl atoms (VS,min = −11.6 or
−12.7 kcal mol−1) of two neighboring molecules to form two
orthogonal I···Cl contacts (p/π-hole HaBs). They are not
equivalent (Figure 1a).
The geometry of a dimer of CF3ICl2 extracted from the

crystal, and that optimized using [M06/aug-cc-PVTZ], is
compared in Figure 1c,d. As can be seen, the nature of the
intermolecular interactions in these dimers do not deviate
significantly from each other, and the chosen theoretical level
faithfully preserves the geometry of the dimer observed in the
crystal. Discrepancies are particularly striking when the ∠C−
I···Cl angles, rather than the intermolecular distances, are the
primary concern. This is reasonable because packing and other
forces between the building blocks play an important role in
shaping the crystal lattice, which is absent in the gas phase
dimers.95 However, both dimer geometries indicate that
orthogonal HaBs between the building blocks are present in
the crystal.
From Figure 1b, it may be seen that the covalently bonded F

and C atoms of the CF3 group in CF3ICl2 are also electrophilic,
and the latter more so than the former. For example, the VS,max
is 8.5, 38.9 and 36.7 kcal mol−1 for the C−F, I−C, and F−C
bond extensions, respectively, indicating that the σ-hole on C

Figure 1. (a) Geometry-based identification of the intermolecular bonding environment around the covalently bonded I in the crystal of CF3ICl2
(CSD ref shown as uppercase letters), showing possible σ- and p/π-hole halogen bonded contacts. (b) The 0.0015 au (electrons bohr−3) mapped
potential (kcal mol−1) on the electrostatic surface of the CF3ICl2 molecule, depicting various electrophilic and nucleophilic regions. (c,d)
Comparison of selected bond distances (Å) and bond angles (degrees) of a dimer extracted from the crystal with that of the geometry optimized
with [M06/aug-cc-pVTZ]. The tiny blue and red circles in (b) represent the local most minima and maxima of potential, respectively, and the
MESP plot is superimposed with QTAIM’s molecular graph of the molecule; the tiny green sphere between bonded atomic basins in (e) represent
the bond critical points and the solid and dotted lines between atomic basins represent the covalent and noncovalent interactions, respectively.
Shown in (f) is the IGM-δginter isosurface plot, displaying attraction between the atom basins.

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is considerably stronger than that on F. Due to the anisotropy
of the charge density along and around the axial portions of the
covalently bonded F atoms, the two neighboring F atoms
facing each other (Figure 1c,d), each from a CF3ICl2, form a
quasilinear σ-hole centered F···F close contact in the dimer’s
equilibrium geometry. The same occurs in the crystal geometry
[r(F···F) values 3.264 Å (crystal) vs 3.108 Å (DFT-M06)].
QTAIM predicts possible intermolecular interactions in

(CF3ICl2)2, based on its molecular graph depicted in Figure 1e.
The long and short I(p/π-hole)···Cl HaBs in the dimer are
characterized by ρb (and ∇2ρb) values of 0.0064 (0.0173) and
0.0073 (0.0193) a.u., respectively. The bond paths generate a
pseudorhombic geometric architecture locally, consisting of a
pair of I−Cl covalent bonds and a pair of I···Cl noncovalent
bonds. The total energy densities, Hb, were 0.00079 and
0.00081 au at the corresponding bond critical points (bcps),
respectively. The small values of ρb indicate weak interactions,
and the signs of ∇2ρb and Hb indicate that these interactions
are of the closed-shell type with recognizable depletion of
charge density around the I(π-hole)···Cl bcps. (1 au of ρb = e/
a03 = 6.748 eÅ−3; 1 au of ∇2ρb = e/a05 = 24.10 eÅ−5; 1 au of Hb
= 1 hartree = 627.5095 kcal mol−1). Similarly, the F(σ-hole)···
F HaB is typified by ρb, ∇2ρb and Hb values of 0.0026, 0.0146,
and 0.0080 au, respectively.
QTAIM reveals F···Cl closeness in the dimer. This may not

be surprising since the lateral portion of the covalently bonded
F in CF3 is weakly electrophilic and the covalently bonded Cl
is fully nucleophilic (cf. Figure 1b). The surface properties
provide a rational basis to appropriate the F···Cl closeness,
which may be a consequence of a Coulombic interaction and is
also a HaB. The ρb, ∇2ρb and Hb values at the F···Cl bcp are
0.0046, 0.0174 and 0.0081 au, respectively. Furthermore, the
F···Cl intramolecular interaction that appears in the monomer
(see the dotted line between the F and Cl atoms in Figure 1b)
persists in one monomer, but is absent in the other monomer
of the dimer due to changes in electronic structure during
dimer formation that cause the development of the F···F close
contact (vide supra). The ρb, ∇2ρb and Hb values at the F···Cl
bcp in the monomer (dimer) are 0.0129 (0.0129), 0.0553
(0.0556), and 0.0022 (0.0022) au, respectively. The
intermolecular interactions revealed by QTAIM may be in
agreement with IGM-δginter’s isosurface plot, Figure 1f.
Furthermore, the latter method discloses the possibility of a
F3C···F tetrel bond; this is supported by the MESP model-
based chemistry (Figure 1b).

3.1.2. Chloro-Fluoro-(Trifluoromethyl)Iodine (CF3ICLF)
Crystal. The nature of intermolecular halogen bonding in the
crystal of chloro-fluoro-(trifluoromethyl)iodine (CF3IClF),
Figure 2a, did not change appreciably compared to that
observed in the crystal of CF3ICl2 (Figure 1a). There are four
p/π-hole and two σ-hole HaBs formed by each hypervalent
iodine atom in CF3IClF with five nearest neighbors, which are
expected because of the positive nature and anisotropy of the
charge density profile on the surface of the I atom in the
molecule (Figure 2b). One of the σ-hole HaBs is substantially
longer than the other, r(I(σ-hole)···F) = 2.870 Å and r(I(σ-
hole)···Cl) = 3.602 Å, and the former is somewhat more
directional than the latter, with ∠C−I···F = 156.7° and ∠C−
I···Cl = 146.0° (and 148.0°). On the other hand, the two p/π-
hole HaBs formed between I and Cl are somewhat shorter than
the remaining two p/π-hole HaBs formed between I and F
(r(I(π-hole)···Cl) = 3.790 Å and r(I(π-hole)···F) = 3.826 Å),
with the former being less directional than the latter (∠C−I···

Cl = 74.2° and ∠C−I···F = 98.0°). These results are not only
in agreement with the description that emerged from the
MESP model (Figure 2b), but also unequivocally demonstrate
that the bond distances associated with the two p/π-hole HaBs
formed between I and F do not conform with IUPAC’s
recommendation41 for HaBs that states “(i) The interatomic
distance between (halogen) X and the appropriate nucleophilic
atom of Y tends to be less than the sum of the vdW radii; and
(ii) The angle R−X···Y tends to be close to 180°, i.e., the HaB
acceptor Y approaches X along the extension of the R−X
bond.” This rationalization is in agreement with the note 9 and
feature f that appeared in our revised definition of the HaB.42

The results of our DFT calculations showed that the
(CF3IClF)2 dimer extracted from the crystal structure did not
retain its crystalline shape when energy minimized in the gas
phase. The interacting CF3IClF molecules in the crystal
(Figure 2c) are rearranged in the gas phase so that the region
of maximum molecular potential could interact favorably. As
shown in Figure 2d, the covalently bonded F atom of one
CF3IClF molecule has come closer to the σ-hole of the I atom
on the extension of the C−I bond in another same interacting
CF3IClF. At the same time, in addition to the formation of the
I(π-hole)···Cl HaB, the covalently bonded Cl atom moves
slightly to attract the nearest most positive carbon of the −CF3
group, creating a σ-hole tetrel bond.34 Both the F−C(σ-hole)···
Cl tetrel bond and I(σ-hole)···F HaB are directional and quasi-
linear, the former more so than the latter because the lateral
side of the covalently bonded F atom in CF3IClF is
simultaneously forming another close contact, F···Cl, with
the nearest Cl atom of a neighboring molecule. The
appearance of this secondary contact is caused by the I(σ-
hole)···F HaB because it is strong (r(I(σ-hole)···F) = 2.800 Å);
even though the lateral portion of the F atoms is negative in
the monomer, its surface is polarized during the course of
forming the I(σ-hole)···F interaction.
Twelve other configurations of the dimer were manually

constructed by displacing slightly the monomers from each
other, away from I’s σ-hole region in CF3IClF. Once energy-
minimized, three of them adopted the same geometry; one is
shown as Conf6 (Figure 2i). Seven of them are shown as
Conf1−Conf7, and the remaining three, Conf8−Conf10, are
shown below (see Figure 3). As can be seen, the I’s p/π-hole in
both the interacting CF3IClF monomers has indeed formed
I(p/π-hole)···F and I(p/π-hole)···Cl HaBs in the dimers in
Conf2 and Conf3 (Figure 2e,f), respectively, including Conf6
(Figure 2i). The intermolecular geometry of Conf6 resembles
the dimer extracted from the crystal (Figure 2c), but its
intermolecular bonding pattern is not as uniform as in the
crystal probably because of the packing forces present in the
latter. This can be explained by the shift of the covalently
bonded F and Cl atoms in both the monomers in the gas-phase
so they can simultaneously engage in an attractive engagement
with the nearest C’s σ-hole of the CF3 group; this highlights
the noninnocent bonding character of covalently bonded
carbon and hence the development of directional C(σ-hole)···
Cl and C(σ-hole)···F tetrel bonds in Conf6. The topology of
intermolecular interactions in Conf6 is similar to that in Conf2,
where the two tetrel bonds are of the C(σ-hole)···F type. The
distances of the C(σ-hole)···Cl and C(σ-hole)···F tetrel bonds
in Conf6 are 3.712 and 3.158 Å, respectively, whereas in Conf2
they are 3.154 and 3.260 Å. They are all directional and quasi-
linear, as can be seen from the values of ∠F−C···F and ∠F−
C···Cl.

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The remaining dimers Conf1, Conf4, and Conf5 consist of
mixed I(σ-hole)···X and I(p/π-hole)···X bonds, and Conf7 is
stabilized purely by a pair of I(σ-hole)···F HaBs. In this case,
the linearity is severely hampered by the competition between
the interacting atomic domains in the process of making the
HaBs. The other three dimers, Conf8-Conf10, which are
geometrically very similar to Conf7, are driven by a pair of I(σ-
hole)···F/Cl HaBs that are also quasi-linear (148.0° < ∠C−I···
Cl/F < 170.0°) with ∠C−I···F is relatively more so than ∠C−
I···Cl (see Figure 3).
QTAIM’s molecular graphs for all the 10 dimers of are

shown in Figure 3a-j. All types of HaBs in these dimers are

validated via the bond path and bcp topologies of the charge
density, yet QTAIM missed all the topological features
necessary for the recognition of the tetrel bonds. What appears
to be a tetrel bond between monomers is captured as an F···F
close contact between the -IClF fragment in one molecule of
CF3IClF and the F atom(s) of the CF3 group in a similar
molecule with which it interacts. These contacts are not
unusual given that the electrostatic potential of F moieties of
the functional group in the monomer are all weakly positive
(Figure 2b) and can engage constructively with nearby
nucleophiles (i.e., on F and Cl of the -IClF fragment). Besides,
QTAIM also predicted the possibility of F···F and Cl···Cl close

Figure 2. (a) Distance-based speculative nature of the 6-fold noncovalent interaction topologies around the iodine atom in CF3IClF in crystalline
CF3IClF (CSD reference shown in uppercase letters). (b) The 0.0015 au isoelectronic density mapped potential of the same molecule, showing the
local minima and maxima (filled tiny circles in blue and red, respectively). (c) A dimer geometry extracted from the crystal, showing the nature of
intermolecular bonding environment between a pair of molecular building blocks. (d−j) DFT-[M06/aug-cc-pVTZ] optimized geometries of the
dimer (Conf1−Conf7) in the conformational space, with selected bond distance (Å) and bond angles (degrees) shown in geometries (a,c−j).
Locations of selected p/π- and/or σ-hole regions on covalently bonded I in CF3IClF are marked in (c−j).

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contacts in the dimer shown in Figure 3b,c, respectively; they
are weak and can be gleaned upon performing an IGM-δginter
analysis with an isovalue <0.005 au (see below). Regardless of
the nature of the interactions involved in the 10 dimers, the
following characteristics were found: Hb (0.0007 au < Hb <
0.0021 au) > 0; ∇2ρb > 0 and ρb < 0.022 au (see Figure 4 for
ρb and ∇2ρb values). These are typical of electrostatically
driven (closed-shell) interactions, with no appreciable degree
of covalency.69,96

The IGM-δginter isosurface plots are shown in Figure 4a−f
only for Conf1−Conf5 to provide evidence of the
intermolecular interactions discussed above, an attempt to
correlate with what was inferred from the MESP model. The
tiny irregular isosurfaces (green volumes) associated with tetrel
bonds in the dimers appear at lower isovalues and disappear
when isovalues around 0.10 au were used. This was not the

case for the isosurfaces representing I···Cl and I···F HaBs,
which are likely to lose their volumetric strength for isovalues
larger than 0.10 au. This means that the tetrel bonds are
secondary interactions while the I···Cl and I···F HBs are
primary interactions. All the bond types coexist at isovalues
around 0.008 au, indicating that the importance of the tetrel
bond cannot be overlooked when considering the overall
stability of the dimer. These bonds play a synergetic role in
dimer formation, helping to explain, for example, why Conf6
(but not Conf1) resembles the dimer shown in Figure 2c.
Similarly, the F···F close-contact in Conf3 persists at low
isovalues around 0.006 au, disappears at isovalues of 0.008 au
(Figure 4d), and has a reasonable volume at 0.005 au (Figure
4c). Furthermore, our assertion that the nonlinearity of the F−
I−Cl skeleton in the CF3IClF monomer is the result of the
involvement of intramolecular C···F and C···Cl tetrel bonds is

Figure 3. (a−j): QTAIM’s molecular graphs for the ten (CF3IClF)2 dimers, Conf1-Conf10, illustrating the bond path (solid and dotted lines in
atom color) and bond critical point (tiny red spheres) topologies of charge density. Values of ρb and ∇2ρb at selected bcps are in a.u. The
intermolecular distances (Å) and angles (degrees) for Conf8−Conf10 are shown in (h−j), together with the total energy Hb density values in a.u.
(see text for discussion). Selected HaB angles are shown for Conf8−Conf10 (see Figure 2 for the remaining dimers).

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confirmed by the occurrence of the circular isosurface volumes
between the respective atomic bases, shown only for Conf3
and Conf5 (Figure 4g,h), whose significance in shaping the
backbone of the CF3IClF molecule cannot be ignored. Similar
intramolecular bonding features between halogen derivatives in
halogenated molecules using isosurface topologies of the
charge density that emanate from the IGM-δginter approach
have been discussed previously.97−99

Our calculations suggests that Conf7 is the most stable and
Conf4 the least stable dimer as determined from their relative
interaction energies (Table 1). The order of stability in the
BSSE corrected ΔE, ΔE(BSSE), is: Conf7 > Conf10 > Conf8
> > Conf5 > Conf1 > Conf9 > Conf2 > Conf3 > Conf6 >

Conf4. The remarkable stability of Conf7, Conf10 and Conf8
is due to the sole involvement of σ-hole interactions and short
bond distances, with ΔE(BSSE) values of −11.52, −9.93 and
−9.65 kcal mol−1, respectively. Conf5 and Conf1 have one σ-
hole and one p/π-hole interaction, among other secondary
interactions, thus ranked as the next set of stable dimers. The
nature of halogen bonding environment in Conf1 is very
similar to that in Conf4, but the latter lacks secondary
interactions, resulting in an energy difference of −4.59 kcal
mol−1 between them. The synergy between many-fold
intermolecular interactions in other dimers places them
beyond the upper limit of weak bonding regime (∼−5 kcal
mol−1). As mentioned above, the dimers that contain a σ-hole

Figure 4. (a−f): IGM-δginter isosurface plots for five conformers of the (CF3IClF)2 dimer, indicating the possible occurrence of C···F/C···Cl tetrel
and I···Cl/I···F HaBs between the interacting monomer entities. Blue/green volumes between atomic basins are isosurfaces, indicating attraction,
reddish areas repulsion. Shown in (g,h) are two representative dimers (Conf3 and Conf5), featuring intramolecular C···F and C···Cl tetrel bonds,
respectively. Labeling of specific atomic basins is shown in (a), whereas the red cross in (d) indicates the loss of F···F contact with an isovalue of
0.008 au, and the red-dotted line indicates the interaction.

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HaB, in addition to contributions from other secondary
interactions, have an enhanced stability.
The inclusion of the effect of dispersion at the level of

Grimme’s DFT−D3 does not significantly increase the
strength of the overall interaction (see ΔE(GD3) and
ΔE(GD3-BSSE) values in Table 1), with contributions ranging
between −0.30 and −0.74 kcal mol−1 [see ΔE(DFT-D3-
BSSE)−ΔE(BSSE) values] which are in the range of the
correction made for the BSSE (−0.34 and −0.62 kcal mol−1;
see the E(BSSE) values). (The range is quantified by the
difference, ΔE(GD3-BSSE) − ΔE(BSSE), which was the
difference between the BSSE corrected interaction energies
without and with the effect of dispersion [(ΔE(BSSE) and
ΔE(GD3-BSSE), respectively]. This means that the uncor-
rected interaction energy, ΔE, is a good approximation if
neither BSSE nor dispersion is taken into account, suggesting
that the formation of the dimers explored is electrostatically
driven.

3.1.3. Design and DIscovery of Molecules Featuring p-/π-
Holes, and Their Dimers, Using DFT Calculations. Halogen
substitution in (CF3ICl2)2 led us to the manual design and
computational discovery of several dimeric structures. We
substituted the halogen derivative in the ICl2 fragment of
F3C−ICl2 (cf. Figure 1b for shape). This resulted in 18 new
dimers that do not include pure σ-hole HaBs. These were fully
relaxed using [M06/aug-cc-PVTZ], and their energy-mini-
mized geometries based on their energy stabilities (see Table 2
for energies), including the two parent dimers, (CF3ICl2)2 and
(CF3IClF)2, are shown in Figures 5a−j and 6k−t.
Physical insight into the regions of the atomic surfaces

responsible for the interacting molecules to form the dimers is
provided in Figure 7a−d. The MESPs for all monomers are not
shown, but the systems of fundamental importance are
considered. A major issue of concern, as Politzer and Murray
noted previously,66 is that the isoelectron density envelope for
calculating the potential is arbitrary.25,100−102 The isoelectron

Table 1. Uncorrected and BSSE Corrected Interaction Energies (ΔE and ΔE(BSSE), Respectively) of the 10 Dimers of
CF3IClF

a,b,c,d

system ΔE ΔE(BSSE) E(BSSE) ΔE(GD3) ΔE(GD3-BSSE) ΔE(GD3-BSSE)-ΔE(BSSE)

Conf1 −9.09 −8.60 −0.49 −9.55 −9.06 −0.46
Conf2 −6.70 −6.09 −0.61 −7.45 −6.83 −0.74
Conf3 −6.11 −5.71 −0.40 −6.57 −6.18 −0.47
Conf4 −4.52 −4.01 −0.51 −5.20 −4.69 −0.68
Conf5 −9.74 −9.26 −0.48 −10.25 −9.77 −0.51
Conf6 −6.07 −5.45 −0.62 −6.78 −6.16 −0.71
Conf7 −11.90 −11.52 −0.38 −12.30 −11.92 −0.40
Conf8 −10.01 −9.65 −0.36 −10.37 −10.01 −0.36
Conf9 −7.73 −7.39 −0.34 −8.03 −7.69 −0.30
Conf10 −10.28 −9.93 −0.35 −10.66 −10.30 −0.37

aIncluded are also the dispersion-incorporated uncorrected and bsse-corrected energies (ΔE(GD3) and ΔE(GD3-BSSE, respectively) and the
differential between ΔE(GD3) and ΔE(GD3-BSSE (ΔE(GD3-BSSE)-ΔE(BSSE)). bSee Figure 3 for Conf1−Conf10. cValues are in kcal mol−1.
dSee eqs 1 and 2 for ΔE’s.

Table 2. Comparison of the [M06/aug-cc-pVTZ] and [M06-GD3/aug-cc-pVTZ] Level Uncorrected and BSSE Corrected
Interaction Energies (ΔE and ΔE(BSSE)) of the 20 Binary Complexes Examineda

Fig. 5/6 dimerb ΔE E(BSSE) ΔE(BSSE) ΔE(GD3) E(BSSE-GD3) ΔE(GD3-BSSE) ΔE(GD3-BSSE)-ΔE(BSSE)

a F3CF2Cl···ClF2CF3 −4.25 0.60 −3.65 −4.89 0.60 −4.29 0.64
b F3CF2Cl···BrF2CF3 −4.35 0.55 −3.80 −4.96 0.55 −4.41 0.61
c F3CBr2I···BrF2CF3 −4.45 0.47 −3.98 −5.12 0.47 −4.65 0.67
d F3CCl2Br···BrCl2CF3 −4.72 0.61 −4.11 −5.50 0.60 −4.90 0.79
e F3CBr2I···BrCl2CF3 −4.82 0.55 −4.27 −5.58 0.54 −5.04 0.77
f F3CBr2I···BrBr2CF3 −4.89 0.57 −4.32 −5.69 0.57 −5.12 0.8
g F3CBr2I···IBr2CF3 −5.00 0.49 −4.51 −5.77 0.49 −5.28 0.77
h F3CCl2I···ICl2CF3 −5.09 0.55 −4.54 −5.86 0.55 −5.31 0.77
i F3CClBrI···IBrClCF3 −5.09 0.53 −4.56 −5.89 0.53 −5.36 0.8
j F3CClI2···I2ClCF3 −5.27 0.46 −4.81 −6.09 0.47 −5.62 0.81
k F3CI2I···BrBr2CF3 −5.30 0.52 −4.78 −6.13 0.51 −5.62 0.84
l F3CCl2Br···ClCl2CF3 −5.86 0.87 −4.99 −6.74 0.87 −5.87 0.88
m F3CF2Br···BrF2CF3 −5.87 0.39 −5.48 −6.32 0.40 −5.92 0.44
n F3CBr2Br···BrBr2CF3 −6.18 0.76 −5.42 −7.07 0.76 −6.31 0.89
o F3CBrI2···I2BrCF3 −6.36 0.54 −5.82 −7.27 0.54 −6.73 0.91
p F3CI3···I3CF3 −6.66 0.46 −6.20 −7.57 0.46 −7.11 0.91
q F3CFBrI···IBrFCF3 −7.02 0.56 −6.46 −7.70 0.55 −7.15 0.69
r F3CFI2···I2FCF3 −7.07 0.48 −6.59 −7.79 0.48 −7.31 0.72
s F3CF2I···IF2CF3 −8.77 0.44 −8.33 −9.18 0.44 −8.74 0.41
t F3CClFI···IFClF3 −9.09 0.49 −8.60 −9.55 0.49 −9.06 0.46

aIncluded are also the bsse energy (e(bsse)), the dispersion-incorporated uncorrected and bsse-corrected energies (δe(gd3)ΔE(GD3) and
ΔE(GD3-BSSEδe(gd3-bsse), respectively) and the differential between δe(gd3-bsse) and δe(bsse)ΔE(GD3) and ΔE(GD3-BSSE
(ΔE(GD3-BSSE)-ΔE(BSSE). Values in kcal mol−1. bSee Figures 5 and 6 for a graphical representation of all the 20 dimers.

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density envelopes commonly used to map potentials, 0.001
a.u,8,90,103 can be a good approximation and often provide
qualitative physical insight into regions on a surface suitable for
the expression of directed, noncovalent interactions.8 However,
this envelope is not suitable for all molecules because each
molecule has its own isoelectronic density surface that roughly
approximates its own vdW surface, and the 0.001 au
isoelectronic density envelope is arbitrary66 and hence may
not adequately define all of them.67

To obtain chemically intuitive maxima and minima of the
potential on the surfaces of the F3C−I−Y2 (Y = F, Cl, Br, I)
molecules, we used three other basis sets, Sadlej pVTZ, def2-
TZVPPD, and 6−311G(d,p). This was prompted by the fact
that the correlation-consistent pseudopotential basis set, aug-
cc-pVTZ (-PP for I), failed to provide the expected features,
especially for molecular entities involving the heavier halogen
derivatives. The first two basis sets, like aug-cc-pVTZ (-PP for
I), have also failed to give the expected maxima and minima of
the potential on the surfaces of the covalently bonded I and C/
F(−CF3) atoms in F3C−I−Y2, unless we used an electron
density envelope close to, or higher than, 0.0014 au. The 6-
311G(d,p) basis set, on the other hand, gave the expected

minimum of potential on the surface of covalently bonded I
that characterizes its p/π-holes, but missed some minima and
maxima of the potentials on the covalently bonded F and C
atoms of the −CH3 group of the molecule. We will address this
issue elsewhere, but here we focus only on the results obtained
using the 6-311G(d,p) basis set and the specific regions on the
surface of the aforementioned molecules that are essential for
understanding the chemical bonding features the monomers
display toward the discovery of the dimers discussed below. It
is worth nothing that the use of higher isoelectronic density
surfaces is necessary since the molecular entities investigated
involve intramolecular interactions; the details of this has been
discussed elsewhere.73,104

As shown in Figure 7, the VS,max value on the surface of the
hypervalent I atom in the F3C-IX2 (X = F, Cl, Br, I) molecules
systematically decreases with the increasing the size of the
halogen derivative in the -IX2 fragment, with a systematic
increase in the strength of I’s σ-hole in the series. This is
concordant with the electron-withdrawing power of the
halogen derivative that increases as F > Cl > Br > I. There
are also two VS,min on the surface of the same I atom that are
characteristics of I’s p/π-hole; they lie on either side,

Figure 5. (a−j) [M06/aug-cc-pVTZ] relaxed geometries of 10 halogenated 1:1 complexes, featuring p/π-hole HaBs and other noncovalent
interactions. Selected bond distances and bond angles are in Å and degrees. Atom labeling is shown only for cases (a,c).

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orthogonal to the C−I covalent bond axis (one shown in
Figure 7a−d). They are reasonably strong, with the VS,min
values that are positive and vary between 16.9 and 15.6 kcal
mol−1. We expected the stability of the p/π-hole of I to have
the same priority as found in the σ-holes of the series, but this
was not the case. The stability preference is as follows: R−Cl >
R−F > R−Br > R−I. Whether this alternation between F3C-IF2
and F3C−ICl2 is due to weak intramolecular interactions
between the −CF3 and −IX2 groups for X = F where the
electron density shift to the −CF3 group is minimal is
uncertain and requires further investigation. QTAIM does not
predict any paths between two groups for X = F (Figure 7a),
unlike for the other three members of the F3C-IX2 family
(Figure 7b-d).
There is no discernible trend in the σ-holes on carbon atoms

of the −CF3 group along the series; they are highly
electrophilic in all four cases. On the other hand, the X atom
bonded to the hypervalent I atom in F3C-IX2 is more

nucleophilic for X = F and with the σ-hole on it neutralized,
and more electrophilic when X = I. When comparing the
strength of the σ-hole along the series, the observed trend was
Cl < Br < I. The absence of the σ-hole on F along the I−F
bond extensions in F3C-IF2 is due to a considerable buildup of
electronic density in the σ-hole regions, causing the
neutralization of the σ-hole on F, as observed in the case of
molecular N2.

103

The p/π-hole HaB geometry seen in (CF3ICl2)2, Figure 1d,
is maintained in the eight dimers shown in Figures 5c−g and
6i−k. The same geometry in the remaining dimers is
significantly deformed as a result of the breaking of the p/π-
hole HaB and the making of new or additional intermolecular
interactions. For example, the dimer in Figure 5b, F3CF2Cl···
BrF2CF3, does not have the pair of p/π-hole HaBs observed in
the crystal of CF3ICl2, Figure 1c. This is because one of the π-
hole HaBs in F3CF2Cl···BrF2CF3 is ruptured upon halogen
substitution and the interacting molecules rearrange to feature

Figure 6. (k−t) [M06/aug-cc-pVTZ] relaxed geometries of another 10 halogenated dimers, featuring p/π-hole HaBs and other noncovalent
interactions. Selected bond distances and bond angles are in Å and degrees. Atom labeling is shown only for cases (a,c). For clarity, secondary
interactions in most of the dimers are not shown (for example, the F−C(σ-hole)···F tetrel bond in (q) is not shown). The locations of p/π- and σ-
hole regions are marked.

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a different scenario of chemical bonding. The stability of the
newly formed dimer, F3CF2Cl···BrF2CF3, results jointly from
the C−Cl(σ-hole)···F and C−Br(π-hole)···F HaBs, and a F−
C(σ)···F tetrel bond.34 The first two are nonlinear (∠C−Cl(σ-
hole)···F = 135.7°) and bent (∠C−Br(π-hole)···F = 69.1°),
respectively, while the latter is markedly linear (F−C(σ)···F =
178.9°); nevertheless, they are all directional interactions.
The C−Cl(σ-hole)···F and C−Br(π-hole)···F HaBs in

F3CF2Cl···BrF2CF3, Figure 5b, is similar to the C−X(σ-
hole)···Y and C−X(π-hole)···Y (X, Y = halogen) HaBs in
F3CF2Br···BrF2CF3 (Figure 6m), F3CFBrI···IBrFCF3 (Figure
6q), F3CFI2···I2FCF3 (Figure 6r), F3CF2I···IF2CF3 (Figure 6s)
and F3CClFI···IFClF3 (Figure 6t). They are all augmented by
secondary interactions; their detailing is beyond the scope of
this study. The last four dimers are the strongest of the 20
dimers in Figures 5a−j and 6k−t, with BSSE-corrected
interaction energies, ΔE(BSSE), of −6.46, −6.59, −8.33 and
−8.60 kcal mol−1, respectively. The energetic advantage of the
strongest dimer F3CClFI···IFClF3 (Figure 6t) over the next
strongest dimer F3CF2I···IF2CF3 (Figure 6s) occurs despite the
presence of a longer C−I(π-hole)···Cl HaB and a longer C−
F(σ-hole)···Cl tetrel bond in the former than in the latter. For
example, the F−C(σ-hole)···Cl and F−C(σ-hole)···F tetrel
bonds in the respective dimers have bond distances (angles) of
3.736 Å (179.8°) and 3.248 Å (176.7°). Similarly, the C−I(π-
hole)···Cl bond distance of 3.743 Å in F3CClFI···IFClF3 is
longer than the C−I(π-hole)···Cl bond distance of 3.230 Å in
F3CF2I···IF2CF3. It is possible that secondary inter/intra-
molecular interactions involving, for example, C···F, F···F/Cl···

F(CF2), or I···F(CF2), etc., underlie the higher stability of
F3CClFI···IFClF3, but this has not been investigated here and
requires further study.
The dimer, F3CF2Cl···ClF2CF3 (Figure 5a), does not

represent an ordered structure. This view is based on the
ordering observed in relation to the C−Cl(π-hole)···Cl
halogen bonded pair and the F···F closeness in the
(CF3ICl2)2 dimer extracted from the crystal of CF3ICl2 (Figure
1c).
The bond distances associated with the C−Cl(π-hole)···F

HaBs in F3CF2Cl···ClF2CF3 are shorter, with r[Cl(π-hole)···F
of 3.150 and 3.327 Å]. The nucleophiles on the covalently
bonded F atoms in -ClF2 in one monomer involved in the
development of these HaBs are being simultaneously shared
with the fluorine of the −CF3 fragment in the other. The latter
leads to the formation of two Cl−F···F(CF2) close-contacts
(r(F···F(CF2)) = 2.896/2.847 Å and ∠(FCl)F···F(CF2) =
131.4°/140.9°). They are quasi-linear and probably σ-hole
centered.
The deductions made from considering the geometries are

not consistent with QTAIM’s molecular graph, Figure 8a. This
indicates the possibility of five F···F close-contacts between the
two −CF3 groups and the -ClF2 fragments of the interacting
monomers. This led us to reinspect the geometry of the dimer,
Figure 5a, and led to the conclusion that the F atom forming
the Cl(π-hole)···F HaB (r(Cl(π-hole)···F) = 3.327 Å) has
close-contact distances of 2.847 (F···F), 2.892 (F···F) and
3.129 Å (C···F) with the adjacent −CF3 group. The latter is
highly directional (∠F3−C(σ)···F = 176.2°) (see Figure 8a)
compared to the first two [(∠Cl−F(σ)···F(CF2) = 140.9° and
∠Cl−F(σ)···F(CF2) = 120.9°]. The view that the tetrel bond
exists is concordant with the positive electrostatic potential
centered at the C atom that occurs along the outermost F−C
bond extension, which is the cause for the development of an
attraction between the F atoms that contribute to formation of
the dimer. The remaining two F···F close-contacts in
F3CF2Cl···ClF2CF3 occur between the two CF3 groups
(r(F···F) = 3.107 Å and (∠(F2C)F(σ)···F(CF2) = 133.4°),
and between the −ClF2 and −CF3 fragments of the interacting
molecules (r(FClF···F) = 2.896 Å and (∠(FCl)F(σ)···F(CF2)/
∠(CF2)F(σ)···F(ClF) = 113.0°), and are not accompanied by
any C···F tetrel bond. The inability of QTAIM to capture the
tetrel bonds in chemical environments as here has been noted
previously.105,106

The F3−C(σ-hole)···X tetrel bond is present in all dimers
(see Figure 8a-t), with its singly or double occupancy, and is a
quasi-linear directional interaction. Its bond distance varies
with the size of the halogen derivative that shares its electron
density rich site with the bonded carbon. The smallest bond
distance is found for the dimer F3CFBrI···IBrFCF3 (Figure
8q). It is comparable to the bond distance range, 3.023−3.248
Å, predicted for the dimers F3CF2I···IF2CF3 (Figure 8s),
F3CFI2···I2FCF3 (Figure 8r) and F3CF2Br···BrF2CF3 (Figure
8m), F3CF2Cl···BrF2CF3 (Figure 8b) and F3CF2Cl···ClF2CF3
(Figure 8a); in these cases, the covalently bonded F in the −
CF3 fragment acts as an electron density rich center. The tetrel
bond in all these six dimers is highly directional, with the angle
of interaction (∠F−C···F) in the range from 175.8 to 179.1°.
When the halogen derivative in the −XYY’ fragment of F3C-
XYY’ in one molecule is involved in creating two Y/Y’···F
contacts with the same participating fragment in a neighboring
molecule, the tetrel bond becomes more directional; this is

Figure 7. [M06/6−311G(d,p)] level MESP of F3C-IX2 (X = F, Cl,
Br, I), obtained upon mapping with the 0.0015 au (electrons bohr−3)
isoelectronic density envelope. The surface maxima and minima of
potential (filled tiny circles in red and blue, respectively) are marked.
Values in kcal mol−1. QTAIM’s bond paths (solid dotted lines in atom
color) and bond critical point (tiny spheres between atoms colored
red) topologies of the charge density are superimposed. Atoms as
spheres are labeled.

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compared to dimers that feature single occupancy of the Y/
Y’···F contact.
Depending on the size of the halogen derivative hosting the

p/π-hole in each molecule for the nucleophilic guest in the
interacting monomer, the intermolecular distance of the p/π-
hole’s HaB changes. Larger halogen derivatives feature longer
bonds, as expected. For instance, the C−I(π-hole)···Cl and C−
I(π-hole)···I π-hole HaBs in F3CClI2···I2ClCF3 (Figure 5j) are
3.801 and 4.221 Å, respectively, whereas each of the two C−
I(π-hole)···I HaBs in F3CI3···I3CF3 (Figure 6p) are 4.207 Å,
which are certainly longer than those formed by Cl and F
atoms in dimers shown in Figure 5a,b. Similarly, the IUPAC
geometric feature has failed to describe the p/π-hole HaBs in
several dimers, viz. F3CBr2I···IBr2CF3 (Figure 5g), F3CBr2I···

BrBr2CF3 (Figure 5f) F3CClBrI···IBrClCF3 (Figure 5i),
F3CClI2···I2ClCF3 (Figure 5j), F3CI2I···BrBr2CF3 (Figure 5k).
This recognition is not true for all C···X tetrel bonds given that
the distance range 3.023−3.231 Å for the C···F tetrel bonds in
some dimers (see Figure 8) is less than, or equal to, the sum of
the vdW radii of the respective bonded atomic basins, 3.23 Å
(rvdW(C) = 1.77 Å and rvdW(F) = 1.46 Å60). Our reasoning is
consistent with Murray et al.,90,91 and our previous com-
ments,17,19,34,35,107 that one should expect favorable inter-
actions in which close contacts can be significantly greater than
the sums of the vdW radii of bonded atomic basins.42

As shown in Table 2, the energy due to BSSE is less than 1.0
kcal mol−1 regardless of the dimers examined, with the
E(BSSE), the energy due to the BSSE, varying between 0.39

Figure 8. (a−t): QTAIM-based molecular graph of 20 dimers, showing possible bonding interactions between interacting monomer molecules via
its bond path and bond critical point topologies of the charge density. The bonding paths between bonded atomic basins (large spheres) are
indicated by atom color, with covalent and noncovalent interactions represented by solid and dotted lines, respectively. The tiny spheres between
atoms in green are bond critical points. Atomic labeling is shown for each entry. The C···X (X = halogen) close contact distances in Å (dotted lines
in red; manually drawn) and angles in degrees are shown, which are ubiquitous in the equilibrium geometry of dimers and are not predicted by
QTAIM.

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and 0.87 kcal mol−1 (for F3CF2Br···BrF2CF3 (Figure 6m) and
F3CCl2Br···ClCl2CF3 (Figure 6l) respectively). Thus, the BSSE
corrected interaction energies, ΔE(BSSE), vary between −3.65
and −8.60 kcal mol−1, for F3CF2Cl···ClF2CF3 (Figure 5a) and
F3CClFI···IFClF3 (Figure 6t), respectively, which are certainly
smaller than the uncorrected interaction energies ΔE of the
corresponding dimers. When the effect of dispersion was taken
into account, the dispersion corrected interaction energy,
ΔE(GD3), increased compared to ΔE. This increase, after
incorporating the effect of the energy due to BSSE (E(GD3-
BSSE)), amounted to between 0.41 and 0.91 kcal mol−1. The
largest dispersion contribution is notable for dimers that
comprise the largest number of heavier halogen atoms [for
example, F3CBrI2···I2BrCF3 (Figure 6o) and F3CI3···I3CF3
(Figure 6p)], yet dispersion is not a major factor that confers
stability to the dimers explored.

3.1.4. Electronic Structures, DOS and Band Structure
Properties of the Crystalline Systems. The crystals of CF3ICl2
(CSD ref COXYIX),57 and (CF3IClF) (CSD ref WO-
WYUC)58 were also examined using periodic boundary
conditions at the PBE/PAW level of theory. The optimized
lattice properties, summarized in Table 3, show the expected
level of agreement between theory and experiment, even
though the lattice is somewhat expanded compared to what
was observed experimentally (see values of lattice volumes). As
a result, the symmetry of the periodic lattice changed from
Cmca to Cmce, yet both belong to the same orthogonal crystal
system. The experimental I···Cl and I···F HaB distances in the
crystals were slightly longer than that of the PBE calculated
geometries (viz. the two inequivalent p/π-hole HaB bond
distances in the crystals and PBE-relaxed geometries: 3.883
(3.926) vs 4.195 (4.290) Å for I···Cl in CF3ICl2 (CSD ref
COXYIX);57 3.826 (3.790) vs 4.149 (4.110) Å for I···Cl (I···F)
in (CF3IClF) (CSD ref WOWYUC)58). The small discrepancy
is not very surprising since more accurate lattice properties can
be obtainable upon invoking high k-mesh and cutoff criteria for
forces on ions and self-consistent loops to converge, and using
a high level of theory. We did not investigate this because of
limited computational resources and the time required for such
a calculation for a large cell containing 56 atoms. Nevertheless,
and as highlighted above, the chemical bonding environment
discussed in Sections 3.1.1 and 3.1.2 for these systems is not
strikingly different from what was calculated using periodic
boundary conditions. Some of the local interactions in the
crystal geometries are illustrated in Figure 9a,b, respectively,
for CF3ICl2 and CF3IClF.
Although the details of the physical properties of the crystals

are not known experimentally, our exploration of the band
structures reveals that both the crystals feature a direct
bandgap, Eg, of 2.15 and 2.78 eV for CF3ICl2 and CF3IClF,
respectively. Clearly, the HaB, and other interactions, play an
important role in these zero-dimensional crystals and suggest
their possible application in optoelectronics, especially in the
visible region. The valence band maximum (VBM) and

conduction band minimum (CBM) have respective energy
strengths of −0.504 (−0.402) and 1.685 (2.381) eV at high-
symmetry Γ-point for CF3ICl2 (CF3IClF), where the character
of the bandgap is direct. The detailed nature of the band
structures of the corresponding crystals are shown in Figure 9c
and d, respectively.
The semiparabolic and flat CBM appears far above the

Fermi level for CF3ICl2 and CF3IClF, respectively; the latter
stands out as the boundary meeting the parabolic VBM. From
DOS spectra (Figure 9e−f), we found that the VBM arises
from the superposition of Cl and I’s p-orbital states for CF3ICl2
(cf. Figure 9e and Table 4). This is not so in the case of
CF3IClF, in which case the VBM is composed equally of the Cl
and I’s p-orbital states, but that of F’s p-orbitals is partially
involved (Figure 9f). Contrarily, the orbital contribution to the
CBM is of this order F(p) < Cl(p) ≤ C(p) < I(p) and Cl(p) <
C(p) < F(p) < I(p) for CF3ICl2 and CF3IClF, respectively,
suggesting that the contribution from the p-orbital states
between Cl, F and C is altered upon the replacement of Cl in
CF3ICl2 by F that constitutes the halogen-bearing fragment
Cl−I−X (X = F, Cl), so affecting the tetrel and halogen
bonding environments in the crystal lattice. In both cases, the
s-orbital contribution to the CBM is marginal (Table 4).

4. DISCUSSION AND CONCLUDING REMARKS
This study has revealed covalently bonded halogen’s p/π- and
σ-hole HaB donating features in the CF3XYY’2 (X, Y, Y’ =
halogen) series of molecules, showing their true combined
involvement in the synthetic design principles toward the
development of ordered crystalline materials. Three of these
chemical systems have been known for the past two decades,
and are prominent molecular building blocks toward the
formation of crystalline CF3IF2, CF3IClF and CF3ICl2. The
remaining CF3XYY’2 models were designed manually via
halogen substitution and computationally discovered as stable
entities. They may be of interest to materials scientists for
synthesis in the future. Periodic calculations with PBE have
enabled us to show that CF3IClF and CF3ICl2 are direct
bandgap materials which may find application in the visible
region of the electromagnetic spectrum.
Some dimers are shown to involve both the p/π- and σ-hole

donors of the hypervalent halogen derivative to form HaBs.
Depending on the size and type of hypervalent halogen
derivative X in the two interacting CF3XYY’2 molecules, one
type of HaB dominates over the other, contributing to the
geometric stability to the dimers investigated. Those are
stabilized by p/π-hole HaBs are relatively ordered and
unaffected by a variety of secondary interactions. Distorted
(or disordered) dimers, especially those involving fluorine and
other mixed halogen environments, show a variety of
secondary interactions, and form weak to moderately strong
dimers. Those driven by both p/π- and σ-hole HaBs are found
to be energetically more stable, an effect of the involvement of
σ-hole HaB. The contribution of dispersion to the interaction

Table 3. Comparison of Experimental and DFT-Calculated Lattice Constants (a, b, c and α/β/γ) and Cell-Volumes of the
Orthorhombic Crystals of CF3ICl2 (CSD Ref. COXYIX),57 and CF3IClF (CSD Ref. WOWYUC)58

system method a/Å b/Å c/Å α = β = γ/degrees cell-volume/Å3

CF3ICl2 Expt57 6.99 7.99 21.18 90° 1182.0
PBE (this work) 7.68 8.05 22.39 90° 1383.4
Expt58 6.90 7.31 20.13 90° 1014.9

CF3IClF PBE (this work) 7.57 7.44 20.86 90° 1173.8

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energy is less than 1 kcal mol−1. While it cannot be totally
overlooked, it is not a major stabilizing factor in shaping the
dimers. In other words, electrostatic and polarization forces are
probably sufficient to explain dimer stability. Murray and

Politzer have shown that a large degree of polarization occurs

once the interaction energies are more negative than −8.0 kcal

mol−1.108

Figure 9. Ball-and-stick models of the PBE-relaxed crystal lattices of (a) CF3ICl2 and (b) CF3IClF. (c,d) represent the band structures, and DOS
spectral features of the corresponding systems, respectively. The Fermi-level (Ef) is marked in (c−f) as a dotted line. Selected bond distances (Å)
and bond angles (degrees) are shown in (a,b).

Table 4. Percentage of Various Orbital Contributions to the VBM and CBM of Crystals of CF3ICl2 (CSD Ref. COXYIX)57 and
CF3IClF (CSD Ref. WOWYUC)58

CF3ICl2 CF3IClF

VBM-character CBM-character VBM-character CBM-character

atom s p d s p d atom s p d s p d
I 0 38.3 0.0 2.9 37.6 3.1 I 0 44.4 0 2.6 39.6 3.7
Cl 0 61.4 0.0 3.0 17.1 0 Cl 0 41.6 0 0.9 9.1 0
C 0 0.0 0.0 7.9 18.5 0 F 0 14.0 0 1.6 13.1 0
F 0 0.6 0.0 0.0 10.1 0 C 0 0.0 0 9.0 20.3 0

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QTAIM recovered most of the halogen-centered intermo-
lecular interactions in all the dimers, especially when p/π- and
σ-hole HaBs between hypervalent halogen derivatives are the
primary synthon. However, there is a major drawback,
especially when correlating with the results of the electrostatic
potential model, and this is most notably related to the tetrel
bond. For instance, in the dimers studied, QTAIM did not
reveal the presence of bond paths or bond critical point
features between the carbon atom of the methyl fluoride group
of the participating F3C-XYY’ molecule and the halogen atom
covalently bonded to the trivalent halogen derivative in a
neighboring molecule. Rather, it predicted the bond paths and
bond critical point features between the nearest F atom of the
methyl fluoride group and the halogen atom covalently bonded
to the trivalent halogen derivative. Although this result
indicates the occurrence of potential F···F contacts, the
number of these contacts depended on the size of the
constituent halogen atoms forming the dimer. The afore-
mentioned disagreement between the results of QTAIM and
MESP is probably because QTAIM sometimes gives
misleading results when analyzing the nature of noncovalent
interactions.70−73 By carefully examining the positive potentials
of the carbon atoms, and the directionality of the interaction,
we were able to show that most of the dimers considered
should have at least one C···X tetrel bond that is incorrectly
predicted by QTAIM to be an F···F contact, a view that
accords with previous observations.71,106 This is in agreement
with IGM-δginter based isosurface topologies developed
between bonded atomic basins.

■ ASSOCIATED CONTENT
Data Availability Statement
This research reported data in the manuscript itself.

■ AUTHOR INFORMATION
Corresponding Author

Pradeep R. Varadwaj − Department of Chemical System
Engineering, School of Engineering, The University of Tokyo,
Tokyo 113-8656, Japan; Molecular Sciences Institute, School
of Chemistry, University of the Witwatersrand, Johannesburg
2050, South Africa; orcid.org/0000-0002-7102-3133;
Email: pradeep@t.okayama-u.ac.jp, prv.aist@gmail.com

Authors
Helder M. Marques − Molecular Sciences Institute, School of

Chemistry, University of the Witwatersrand, Johannesburg
2050, South Africa; orcid.org/0000-0003-1675-3835

Arpita Varadwaj − Department of Chemical System
Engineering, School of Engineering, The University of Tokyo,
Tokyo 113-8656, Japan; orcid.org/0000-0001-8779-
789X

Koichi Yamashita − Department of Chemical System
Engineering, School of Engineering, The University of Tokyo,
Tokyo 113-8656, Japan; orcid.org/0000-0002-6226-
3194

Complete contact information is available at:
https://pubs.acs.org/10.1021/acs.cgd.4c00448

Author Contributions
Conceptualization, project design, and project administration,
P.R.V.; formal analysis and investigation, P.R.V.; software�
P.R.V., H.M.M. and K. Y.; supervision, P.R.V.; writing�
original draft, P.R.V.; writing�review, editing, and discussion,

P.R.V., H.M.M., A.V., and K.Y. All authors have read,
understood and agreed to the published version of the
manuscript.
Notes
The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS
This work was entirely conducted using various laboratory
facilities provided by the University of Tokyo and the
University of the Witwatersrand. P.R.V. is currently affiliated
with the University of the Witwatersrand (RSA) and Nagoya
University (Japan). A.V. is currently affiliated with Tokyo
University of Science (Japan). K.Y. is currently affiliated with
Yokohama City University (Japan). H.M.M. thanks the
University of the Witwatersrand for funding. All authors
thank Professors Jane S. Murray and Irek Grabowski, as well as
the three reviewers, for their fruitful suggestions that have
undoubtedly improved the scientific quality of this ms.

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