The Interaction of Radicals with Ï-Holes

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The Interaction of Radicals with #-Holes Timothy Clark J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b01133 • Publication Date (Web): 27 Mar 2019 Downloaded from http://pubs.acs.org on March 27, 2019

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The Journal of Physical Chemistry

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The Interaction of Radicals with -Holes Timothy Clark* Computer-Chemistry Center, Friedrich-Alexander-University Erlangen-Nürnberg, Nägelsbachstraße 25, 91052 Erlangen, Germany. [email protected]

Abstract: The non-covalent interactions of the CH3, Cl, CF3 and C(CH3)3 radicals with CF3X molecules (X = Cl, Br, I) have been investigated using CCSD(T)/aug-cc-pVTZ energy calculations on MP2/aug-cc-pVTZ-optimized geometries. The electrophilic chlorine atom prefers to complex with the equatorial belt of the heavier halogen X, whereas the nucleophilic radicals CH3 and C(CH3)3 coordinate preferentially with the -hole of X to give C3v complexes. Complexation energies are generally small, ranging up to 5 kcal mol1 for CF3I with either the chlorine atom or the tBu radical. Within the continuum from pure one-electron (SOMO-LUMO) to pure three-electron (SOMO-HOMO) bonds, the results can be interpreted in terms of predominantly one-electron bonds for nucleophilic radicals but closer to threeelectron bonds for the chlorine atom. The trifluoromethyl radical binds very weakly via interhalogen interactions; the carbon radical center plays no role in the bonding.

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1. INTRODUCTION Leo Radom contributed significantly to our understanding of odd-electron bonds and coined the term “hemibond” for three-electron bonds.1 Leo’s computational discovery of stable neutral three-electron bonded species2 made a reevaluation of the theory of odd-electron bond strengths necessary.3 Odd-electron bonds are unusual because the common qualitative molecular-orbital approach proves not to be able to rationalize the trends in bond strengths well,4 whereas valence-bond resonance theory provides an excellent description.3,5,6-8 Because the oddelectron bond energy falls off exponentially with increasing electron-transfer energy,9 neutral odd-electron bonds are generally weak but can be moderately strong if the ion-pairing energy is particularly favorable.2,3 Weak intermolecular interactions, however, often have important consequences, as shown by the importance of -hole bonding,10-17 which can be treated as a simple electrostatic (including polarization) interaction plus dispersion.18 It has recently been shown19,20 that this simple model can treat strong interactions adequately, in addition to the weak non-covalent bonds for which it was conceived. However, -hole bonding has been investigated almost exclusively for closed-shell species. It is therefore appropriate to investigate the interaction of free radicals with the prototypical hole substrates CF3X (X = Cl, Br, I) on the occasion of Leo Radom’s 75th birthday. Scheme 1 shows the bonding properties of CF3X schematically.

Polar flattening, enhanced dispersion F

F C

X

Electrophilic -hole

F

Nucleophilic equatorial belt Scheme 1: Schematic view of the bonding properties of the heavier halogen X (= Cl, Br, I) in CF3X.

The purpose of this study is not to provide a formal bonding analysis of the interactions of radicals with -hole systems but rather to investigate the structures and energetics of complexes between representative radicals and trifluoromethyl halides at a satisfactory level of theory. The energetic and structural results are new and literature searches have neither revealed experimental nor theoretical studies on these systems. Because of the unique nature of the oddACS Paragon Plus Environment

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electron interactions in the subject complexes, this work has purposely been limited to reporting the structures and interaction energies of the complexes and an analysis within the framework of the existing resonance theory of odd-electron bonding.3,5,6-8 The anisotropic distribution of electron density around the halogen X10,13 leads to the electrostatic -hole collinear with the C-X bond but also to a nucleophilic belt around the equator of X. Polar flattening21,22 leads to enhanced dispersion collinear with the C-X bond because the bonding partner can approach X more closely from this direction.23-25 The question therefore arises as to how free radicals form weakly bonded complexes with CF3X; i.e. whether electrophilic radicals prefer collinear complexes and nucleophilic radicals to complex around the equatorial belt of X, or whether dispersion in the collinear direction dominates the interaction. We have therefore investigated the interactions of CF3Cl, CF3Br and CF3I with CH3, CF3, Cl and C(CH3)3 as representative radicals with different electronic characteristics. 2. COMPUTATIONAL METHODS Geometries were optimized using second order Møller-Plesset theory26-28 with the aug-ccpVTZ basis set.29,30 Iodine calculations used the aug-cc-pVTZ pseudopotential basis set31 taken from the EMSL Basis-Set Exchange.32-34 Optimized geometries were characterized by calculating their normal vibrations within the harmonic approximation. The number of imaginary frequencies zero for each structure shown in Table 1 except for the C3v complexes of Cl and CF3, which have degenerate imaginary bending modes. Energies were refined at the coupled-cluster level with single and double excitations with a perturbational correction for triple excitations (CCSD(T)),35-37 also with the aug-cc-pVTZ basis set using the MP2/aug-ccpVTZ-optimized geometries. Single-point CCSD(T) calculations were also performed with a counterpoise correction38,39 to take basis-set superposition error (BSSE) into account; these calculations are designated CCSD(T)-cp/aug-cc-pVTZ. All calculations used the Gaussian16 series of programs.40 The CCSD(T)-cp interactions energies should be accurate, although some uncertainty remains because of the open-shell nature of the complexes studied. In the absence of experimental data, however, the results presented here represent the best estimates of the binding energies of the complexes considered. Ion-pairing energies were calculated using an atom-centered point-charge model. For this model, atomic charges were calculated for the oxidized and reduced CF3X and R moieties at their geometries in the optimized complex. Potential-derived charges calculated using the MerzSingh-Kollman scheme41,42 and atomic radii from the Universal Force Field43 were used to



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calculate the ion-pairing energies in a simple Coulomb model at the MP2/aug-cc-pVTZoptimized geometries. 3. RESULTS AND DISCUSSION Two initial complex geometries were used for the optimizations; one (C3v) with the radical complexed collinear with the C-X bond and a second (Cs) in which the C-X-R angle (R = central atom of the radical) was initially 90°. The two geometries are designated by their initial point groups (C3v and Cs) in the following. The Cs structures distorted to C1 symmetry for complexes with the trifluoromethyl radical (the Cs structure is a transition state in these cases). Table 1 shows the calculated energies for the radical complexes.


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5 Table 1: Calculated interaction energies (kcal mol1) including the MP2/aug-cc-pVTZ-calculated zeropoint energy. All calculations used the aug-cc-pVTZ basis set at the MP2/aug-cc-pVTZ-optimized geometry. Counterpoise calculations are designated “-cp”.

a

CF3Cl...CH3 C3v CF3Cl...CH3 Cs

MP2 -0.76 -0.70

CCSD(T) -0.78 -0.79

CCSD(T)-cp -0.55 -0.40

CF3Cl...Cl C3v CF3Cl...Cl Cs

-0.26a -1.27

-0.19 -1.19

0.02 -0.75

CF3Cl...CF3 C3v CF3Cl...CF3 C1

-0.51a -1.28

-0.60 -1.42

-0.21 -0.72

CF3Cl...C(CH3)3 C3v CF3Cl...C(CH3)3 Cs

-3.26 -3.30

-2.91 -3.21

-2.29 -2.12

CF3Br...CH3 C3v CF3Br...CH3 Cs

-1.36 -0.94

-1.35 -1.00

-0.66 -0.07

CF3Br...Cl C3v CF3Br...Cl Cs

-0.37a -2.24

-0.26 -2.27

-0.80 -1.32

CF3Br...CF3 C3v CF3Br...CF3 C1

-0.90a -1.61

-1.00 -1.72

-0.20 -0.71

CF3Br...C(CH3)3 C3v CF3Br...C(CH3)3 Cs

-5.95 -4.50

-5.24 -4.23

-3.14 -2.10

CF3I...CH3 C3v CF3I...CH3 Cs

-2.14 -1.13

-2.12 -1.36

-1.16 -0.10

CF3I...Cl C3v CF3I...Cl Cs

-1.64 -6.94

-1.47 -6.15

-0.95 -4.66

CF3I...CF3 C3v CF3I...CF3 C1

-1.23 -1.68

-1.30 -1.77

-0.20 -0.71

CF3I...C(CH3)3 C3v CF3I...C(CH3)3 Cs

-8.47 -5.09

-7.54 -4.71

-4.87 -2.28

Structure has two imaginary frequencies (the degenerate C-X-R bending modes).

Figure 1 shows the geometries obtained for CF3X…CH3 (X = Cl, Br, I)



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Figure 1: MP2/aug-cc-pVTZ-optimized geometries of the C3v and Cs CF3Cl…CH3, CF3Br…CH3 and CF3I…CH3 complexes. All six structures are minima. The CCSD(T)/aug-cc-pVTZ/MP2/aug-cc-pVTZ calculated interaction energies with counterpoise and zero-point energy corrections are given in kcal mol1.

The C3v structures are the more stable for in all three cases but they are weakly bound with calculated CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ + ZPE interaction energies of only 0.6, 0.7 and 1.2 kcal mol1 for X=Cl, Br and I, respectively. Notably, the I…C distance in the CF3I complex is marginally shorter than Br…C in the CF3Br equivalent. These distances are both approximately 10% shorter than the sums of the van der Waals radii (3.55 and 3.68 Å for Br-C and I-C, respectively).44,45 The Cs complexes are 0.2, 0.6 and 1.1 kcal mol1 less stable than the C3v structures for the CF3Cl, CF3Br and CF3I complexes, respectively, and exhibit very weak C-H…X (X=F, Br, I) hydrogen bonds as the preferred mode of binding. The Cs-complex shows only C-H…F interactions for CF3Cl, whereas one hydrogen atom in the CF3Br and CF3I complexes interacts weakly with the equatorial belt of the heavy halogen. No minima were found in which the central carbon of the radical coordinates directly with the equatorial belt of bromine or iodine. The electrophilic chlorine atom binds significantly more strongly than the methyl radical to the CF3X compounds and exhibits a different geometrical preference, as shown in Table 1 and Figure 2.


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Figure 2: MP2/aug-cc-pVTZ-optimized geometries of the C3v and Cs CF3Cl…Cl, CF3Br…Cl and CF3I…Cl complexes. All structures are minima except C3v CF3Br…Cl and CF3Br…Cl·, which have two degenerate imaginary C-X…Cl bending modes. The CCSD(T)/aug-cc-pVTZ/MP2/aug-cc-pVTZ calculated interaction energies with counterpoise and zero-point energy corrections are given in kcal mol1.

In all three cases, and in contrast to the complexes with CH3·, the Cs complexes are the more stable. The chlorine atom binds more strongly to the trifluoromethyl halides than methyl, with calculated interaction energies of -0.8, -1.3 and -4.7 kcal mol1 with CF3Cl, CF3Br and CF3I, respectively. The Cl…Cl, Cl…Br and Cl…I distances (3.24, 2.99 and 2.70 Å, respectively) are approximately 8, 17 and 28% shorter than the sums of the van der Waals radii (3.50, 3.60 and 3.73 Å) and decrease in the reverse order to that of the van der Waals distances. The Cl…I contact is almost 0.3 Å shorter than that with bromine, which is in turn 0.25 Å shorter than the Cl…Cl contact. The C-X…Cl angles are close to 90°, indicating a direct interaction between X and the chlorine atom. The CF3I…Cl· interaction energy is equivalent to that of a strong hydrogen bond, whereas those for CF3Cl…Cl· and CF3Br…Cl· are significantly weaker, but still stronger than those found for the methyl radical. The C3v complexes are weakly bound with van der Waals X…Cl contacts, although the CF3I equivalent is significantly (-1.0 kcal mol1) bound with an I…Cl contact 5% shorter than the sum of the van der Waals radii. The optimized geometries obtained for the CF3X…CF3· complexes are shown in Figure 3.



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Figure 3: MP2/aug-cc-pVTZ-optimized geometries of the C3v and “Cs” CF3Cl…CF3, CF3Br…CF3 and CF3I…CF3 complexes. All structures are minima except C3v CF3Cl…CF3 and CF3Br…CF3·, which have two degenerate imaginary C-X…C bending modes. The “Cs” structures deviate from Cs symmetry to give one short F…F distance (marked). The CCSD(T)/aug-cc-pVTZ/MP2/aug-cc-pVTZ calculated interaction energies with counterpoise and zero-point energy corrections are given in kcal mol1.

As for the complexes with the chlorine atom, those with the trifluoromethyl radical prefer the “Cs” geometry, which, however, does not retain Cs symmetry but rather distorts to give one short intermolecular X…F contact and one short fluorine contact24 between fluorine atoms of the radical and CF3X. The X…F and F…F contacts are all longer than the sums of the van der Waals radii. The interaction energies are consistent with these distances, all being close to 0.7 kcal mol1. The electrophilic tbutyl radical forms strong complexes with CF3X and generally prefers the C3v geometry, as shown in Figure 4.


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Figure 4: MP2/aug-cc-pVTZ-optimized geometries of the C3v and C1 CF3Cl…C(CH3)3, CF3Br…C(CH3)3 and CF3I…C(CH3)3 complexes. All structures are minima. The CCSD(T)/aug-cc-pVTZ/MP2/aug-cc-pVTZ calculated interaction energies with counterpoise and zero-point energy corrections are given in kcal mol1.

The tBu radical forms strong C3v complexes (interaction energies of 2.3, 3.1 and 4.9 kcal mol1 for X = Cl, Br and I, respectively). The X…C distance is significantly lower than the sums of the van der Waals radii (3.45, 3.55 and 3.68 Å for X = Cl, Br, I, respectively) in all three C3v complexes. The shortening amounts to -14, -19 and -27% of the sum of the van der Waals radii for C…Cl, C…Br and C…I, respectively. The Cs complexes are linked by C-H…F or C-H…X hydrogen bonds and have interaction energies (2.2  0.1 kcal mol1) comparable with common hydrogen bonds. 4. DISCUSSION 4.1. BONDING AND INTERACTION ENERGIES Chemical bonding is traditionally discussed in terms of qualitative molecular-orbital (MO) pictures, which, however, have not yet been able to rationalize odd-electron bonding.3,4,8,9 The most successful approach has been resonance theory using different redox resonance structures.3,5-8 In the case of the complexes described above, we can distinguish between electrophilic and nucleophilic radicals, which in an oversimplified picture would lead to threeelectron bonds with the highest occupied molecular orbital (HOMO) of CF3X, shown in Figure 5a, or a one-electron bond with the lowest occupied molecular orbital (LUMO), shown in Figure 5b. In reality, odd-electron interactions represent a continuum between the two extreme



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situations shown in Figure 5. In many cases, however, one interaction dominates, so that a coarse assignment as a one- or three-electron interaction can be made. This situation is analogous, for instance, to the analysis used for the Woodward-Hoffmann rules.

Figure 5: Schematic MO-diagrams for the interactions of (a) an electrophilic radical with CF3X via a three electron bond and (b) of a nucleophilic radical via a one-electron bond.

These pictures translate into the following resonance hybrids for three- and one-electron bonds, respectively. Three-electron bond, electrophilic radical:

CF3X + R g  CF3X + g+R -

One-electron bond, nucleophilic radical:

CF3X + R g  CF3X  g+R 

The calculated vertical ionization energies are accurate to within 0.3 eV, as shown in Table S3 of the Supporting Information. No comparison with experiment is possible for vertical electron affinities. Electron-transfer energies have been calculated according to the stablished procedure3,46,47 Table 2 shows that the preferred direction of electron transfer for R = CH3· and C(CH3)3· is clearly reduction of CF3X and oxidation of the radical, whereas the reverse direction is strongly favored for R = Cl·. There is no uniform trend for R = CF3·; CF3Cl and CF3Br prefer to accept an electron from CF3·, whereas CF3I prefers to be oxidized. These results agree with all but one (CF3I…CF3) of the structural preferences shown in Table 1 and Figures 1-4. Complexes with the chlorine atom, for which reduction of the radical is preferred, all form stable Cs complexes, whereas for those that prefer oxidation of the radical (R = CH3 and C(CH3)3) are more stable in the linear, C3v geometry. Complexes with CF3 all prefer C1 ACS Paragon Plus Environment

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structures but are weakly bound. The very weakly bound one-electron bonded C3v structures (binding energy = approximately 0.2 kcal mol1) compete with slightly more stable C1 structures with halogen-halogen contacts (binding energy = approximately 0.7 kcal mol1). The latter have neither one- nor three-electron bond character (the central carbon of the radical is directed away from CF3X) and comply with the binding mode found previously for gempolyfluoro compounds.24 Thus, for R = CF3, there is no observable competition between oneand three-electron bonded species. Table 2: Experimental48 ionization potentials (IP, eV) and electron affinities (EA, eV) for the CF3X compounds and the complexing radicals. The energies for electron transfer in both directions are given as sums of the appropriate ionization potential, electron affinity and ion-pairing energy. The more favorable direction is indicated in bold for each complex.

Species CF3Cl CF3Br CF3I CH3

C3v Cs C3v CF3 Cs C3v Cl Cs C(CH3)3 C3v Cs

IP 12.6 11.09 10.38

EA 0.20 0.91 1.57

9.84

0.08

8.76

1.82

12.97

3.61

6.70

-0.16

Electron-transfer energy (eV) CF3X+. R CF3Cl CF3Br CF3I 9.08 7.79 6.41 9.51 8.98 7.57 8.79 7.60 6.27 9.14 8.13 7.05 5.89 4.75 3.45 5.31 3.91 2.32 10.18 9.01 7.72 10.30 9.25 8.04

CF3X. R+ CF3Cl CF3Br 6.76 6.06 7.69 7.27 8.00 7.33 8.79 8.64 12.23 11.69 12.27 11.77 4.59 4.09 5.31 5.17

CF3I 5.85 6.74 7.06 8.00 11.37 10.86 3.88 4.42

The competition between the different possible types of interaction in the CF3X…R complexes makes analyses complex and equivocal. However, the maximum interaction energies of approximately 5 kcal mol1 make extensive analyses unnecessary. However, odd-electron bond theory predicts that the interaction energy in a one- or three-electron bond should fall off exponentially with increasing electron-transfer energy, EET, between the bonding partners.3,9 The interaction energy between A and B, EAB, is given by

E AB

D  DBB  2 ; AA e 2

EET D AA DBB

(1)

where DAA and DBB are the one-or three-electron interaction energies of the A-A and B-B dimers, respectively. If we make the coarse assumption that DAA and DBB are roughly constant for the systems considered, log(EAB) should correlate roughly with EET. Figure 6 shows a plot of the logarithm of minus the interaction energy of the most stable structure vs the most ACS Paragon Plus Environment


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favorable ET-energy for each complex. Figure 6 also shows the plot obtained if the chlorineoxidation ET-energy is used, rather than the more favorable reduction energy. The three data points for complexes with the chlorine atom are also shown using EET for the oxidation of chlorine, rather than the more favorable reduction. The data points obtained using the most favorable EET-value in each case (solid circles) gives a moderate correlation (R2 = 0.76), in accord with the expectations. Both EET-correlations for the chlorine atom give good correlations (R2 = 0.991 for chlorine oxidation and 0.969 for reduction) but the line for chlorine reduction lies far closer to the data points for the other radicals. All in all, Figure 6 can be understood as moderately convincing support for the one- and three-electron bonding model proposed above.

Figure 6: Correlation of log10(-Eint) vs EET. The solid circles and the black dashed regression line are for all complexes with the most favorable EET (i.e. that shown in bold in Table 2). The crosses and the red dashed regression line indicate the data points for the reduced chlorine atom and the blue triangles and dashed line those for the oxidized chlorine atom. R2 values are shown in the same color as the regression line.

4.2. SPIN POLARIZATION AND DELOCALIZATION Just as polarization plays an important role in -hole bonding,49,50 spin polarization can be expected to be important in the complexes discussed here. Figure 7 shows the MP2/aug-ccACS Paragon Plus Environment

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pVTZ-calculated spin densities for the most stable forms of CF3I…CH3, CF3I…C(Me3)3 and CF3I…Cl. All three complexes show extensive spin delocalization that can be interpreted as CF3I…R spin polarization. However, the three-electron bonded CF3I…Cl complex shows very extensive delocalization of the -spin density (blue) over the chlorine and iodine atoms in addition to polarization of the C-I bond. The magnitude of this delocalization is surprising considering the weakness (-4.7 kcal mol1) of the bond. This can be understood as an expression of the importance of the ion-pair structure in the CF3I + Clg  CF3I + g+Cl- resonance scheme.

Figure 7: 0.001 a.u. isodensity plots of the - (blue) and - (red) MP2/aug-cc-pVTZ spin densities for the complexes of CF3I with CH3, C(CH3)3 and Cl.

5. CONCLUSIONS The radicals investigated form weak complexes with CF3X compounds; the strongest have approximately the interaction energy of standard hydrogen bonds and are formed with CF3I. The interaction energies can be understood in terms of the notional extreme cases of one- (with nucleophilic radicals) or three-electron (with electrophilic radicals) bonding. Within such a model, the interaction energy depends approximately exponentially on the calculated electrontransfer energy in the appropriate direction. This is from CF3X to the radical for the chlorine atom, in the reverse direction for the methyl and tbutyl radicals and can be in either direction for the trifluoromethyl radical, which generally prefers to form weak complexes via F-bridges to fluorine and X-atoms of CF3X.



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Although not discussed above, it is likely that a significant component of the interactions energies for X = I is due to dispersion. Spin polarization/delocalization is far more extensive than the small interaction energies would suggest. Seen in the wider context of analyzing weak interactions, the complexes discussed here are unusual because of their open-shell character. The resonance theory of odd-electron bonds used here was originally developed9 for stronger three-electron bonds and has since3 been used for weaker interactions. Note that the bonding has neither been analyzed in terms of a purely electrostatic model51 nor with respect to concepts such as covalency or charge transfer. This is because these concepts are formally indistinguishable from pure electrostatic polarization in weak complexes,52,53 so that the three concepts (polarization, covalency and charge transfer) are equivalent in weak complexes. Likewise, topological analyses of the electron density have not been performed because, for instance, the Poincaré-Hopf relationship dictates that a bond critical point (BCP) would be found between the radical and the trifluoromethyl halide. This BCP, however, has nothing to do with bonding but is simply a consequence of the topology of any scalar field and the symmetry of the system.54 The great unknown in the interactions discussed above is spin polarization. It constitutes the difference to weak non-covalent bonding in closed-shell complexes and disqualifies any analysis based on “closed-shell” principles. Even Ruedenberg’s classical work on the physical nature of the chemical bond55 did not include a system in which spin-polarization is possible, so that it also provides no guidance to the contribution of different stabilization mechanisms. Note also that the term “-hole” refers to the electrostatic properties of bonded halogens and other elements of the second and higher long periods.10 The term “-hole bonding” has come to be associated with an interpretation of non-covalent interactions that consists of a Coulomb interaction between the mutually polarized bonding partners and dispersion.18 This work does not treat “-hole bonding” in that sense but rather the interaction of systems that exhibit -holes with radicals. Finally, what consequences can we expect from the interactions investigated here? The interaction energies calculated for the most strongly bound complexes are comparable with those for classical hydrogen bonds. Such interaction energies would, for instance, be significant in determining the specificity of radical reactions if reactive complexes are formed. More important consequences can be expected in organic electronics applications. Charged and


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neutral radicals are often formed, for instance in organic photovoltaics, so that stabilized radical traps may act as, for instance, electron traps analogously to fullerene van der Waals dimers.56 6. SUPPORTING INFORMATION Total, zero-point and interaction energies for the complexes calculated, MP2/aug-cc-pVTZoptimized geometries for monomers and complexes, calculated ion-pairing and electrontransfer energies and a comparison of calculated and experimental ionization potentials and electron affinities. 7. ACKNOWLEDGMENTS This work was supported by the Solar Technologies go Hybrid (SolTech) initiative of the Bavarian State Government. 8. REFERENCES 1. Gill P. M. W.; Radom L. Structures and Stabilities of Singly Charged Three-Electron Hemibonded Systems and their Hydrogen-Bonded Isomers. J. Am. Chem. Soc. 1988, 110, 4931–4941. 2. McKee M. L.; Nicolaides, A.; Radom, L. A Theoretical Study of Chlorine Atom and Methyl Radical Addition to Nitrogen Bases: Why Do Cl Atoms Form Two-Center-Three-Electron Bonds Whereas CH3 Radicals Form Two-Center-Two-Electron Bonds? J. Am. Chem. Soc. 1996, 118, 10571–10576. 3. For a recent review, see Clark, T. Odd-Electron Bonds, ChemPhysChem, 2017, 18, 2766– 2771. 4. Baird, N. C.; Three-Electron Bond. J. Chem. Educ. 1977, 54, 291–293. 5. Hiberty, P. C.; Humbel, S.; Archirel, P. Nature of the Differential Electron Correlation in Three-Electron Bond Dissociations. Efficiency of a Simple Two-Configuration Valence Bond Method with Breathing Orbitals. J. Phys. Chem. 1994, 98, 11697–11704. 6. Harcourt, R. D. Valence Bond and Molecular Orbital Descriptions of the Three-Electron Bond. J. Phys. Chem. A 1997, 101, 2496–2501; Additions and corrections p. 5962. 7. Harcourt, R. D. Valence Bond and Molecular Orbital Descriptions of the Three-Electron Bond: Additions and Corrections. J. Phys. Chem. A 1997, 101, 5962-5962.



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7. Hiberty, P. C.; Humbel, S.; Danovich, D.; Shaik, S. What Is Physically Wrong with the Description of Odd-Electron Bonding by Hartree-Fock Theory? A Simple Nonempirical Remedy. J. Am. Chem. Soc. 1995, 117, 9003–9011. 8. Hiberty, P. C.; Shaik, S. Breathing-Orbital Valence Bond Method – a Modern Valence Bond Method that Includes Dynamic Correlation. Theor. Chem. Acc. 2002, 108, 255–272. 9. Clark, T. Odd-Electron -Bonds. J. Am. Chem. Soc., 1988, 110, 1672-1678. 10. Clark, T.; Hennemann, M.; Murray, J. S.; Politzer, P. Halogen Bonding: The σ-Hole. J. Mol. Model. 2007, 13, 291–296. 11. Politzer, P.; Murray, J. S.; Clark, T. Halogen Bonding: An Electrostatically-Driven Highly Directional Noncovalent Interaction. Phys. Chem. Chem. Phys., 2010, 12, 7748-7757. 12. Murray, J. S.; Lane, P.; Clark, T.; Riley, K. E.; Politzer, P. Σ-Holes, π-Holes and Electrostatically-Driven Interactions. J. Mol. Model. 2012, 18, 541-548. 13. Clark, T. ‐Holes. WIREs Comput. Mol. Sci. 2013, 3, 13–20. 14. Politzer, P.; Murray, J. S. Halogen Bonding: an Interim Discussion. ChemPhysChem, 2013, 14, 278-294. 15. Politzer, P.; Murray, J. S.; Clark, T. Halogen Bonding and other σ-Hole Interactions: A Perspective. Phys. Chem. Chem. Phys. 2013, 15, 11178-11189. 16. Politzer, P.; Murray, J. S.; Clark, T. σ-Hole Bonding: A Physical Interpretation. Top. Curr. Chem. 2015, 358, 19–42. 17. Politzer, P.; Murray, J. S.; Clark, T.; Resnati, G. The σ-Hole Revisited. Phys. Chem. Chem. Phys. 2017, 19, 32166-32178. 18. Clark, T. Halogen Bonds and σ-Holes. Faraday Disc. “Halogen Bonding in Supramolecular and Solid State Chemistry”, 2017, 203, 9-27. 19. Clark T.; Heßelmann, A. The Coulombic σ-Hole Model Describes Bonding in CX3I…Y– Complexes Completely. Phys. Chem. Chem. Phys. 2018, 20, 22849-22855. 20. Clark, T.; Murray J. S.; Politzer, P. The σ-Hole Coulombic Interpretation of Trihalide Anion Formation. ChemPhysChem 2018, 19, 3044-3049. 21. Stevens, E. D. Experimental Electron Density Distribution of Molecular Chlorine. Mol. Phys. 1979, 37, 27–45. ACS Paragon Plus Environment

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Scheme 1: Schematic view of the bonding properties of the heavier halogen X (= Cl, Br, I) in CF3X. 100x51mm (300 x 300 DPI)


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Figure 1: MP2/aug-cc-pVTZ-optimized geometries of the C3v and Cs CF3Cl…CH3, CF3Br…CH3 and CF3I…CH3 complexes. All six structures are minima. The CCSD(T)/aug-cc-pVTZ/MP2/aug-cc-pVTZ calculated interaction energies with counterpoise and zero-point energy corrections are given in kcal mol-1. 338x190mm (96 x 96 DPI)



Figure 2: MP2/aug-cc-pVTZ-optimized geometries of the C3v and Cs CF3Cl…Cl, CF3Br…Cl and CF3I…Cl complexes. All structures are minima except C3v CF3Br…Cl and CF3Br…Cl·, which have two degenerate imaginary C-X…Cl bending modes. The CCSD(T)/aug-cc-pVTZ/MP2/aug-cc-pVTZ calculated interaction energies with counterpoise and zero-point energy corrections are given in kcal mol-1. 338x190mm (96 x 96 DPI)


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Figure 3: MP2/aug-cc-pVTZ-optimized geometries of the C3v and “Cs” CF3Cl…CF3, CF3Br…CF3 and CF3I…CF3 complexes. All structures are minima except C3v CF3Cl…CF3 and CF3Br…CF3·, which have two degenerate imaginary C-X…C bending modes. The “Cs” structures deviate from Cs symmetry to give one short F…F distance (marked). The CCSD(T)/aug-cc-pVTZ/MP2/aug-cc-pVTZ calculated interaction energies with counterpoise and zero-point energy corrections are given in kcal mol-1. 338x190mm (96 x 96 DPI)



Figure 4: MP2/aug-cc-pVTZ-optimized geometries of the C3v and C1 CF3Cl…C(CH3)3, CF3Br…C(CH3)3 and CF3I…C(CH3)3 complexes. All structures are minima. The CCSD(T)/aug-cc-pVTZ/MP2/aug-cc-pVTZ calculated interaction energies with counterpoise and zero-point energy corrections are given in kcal mol-1. 338x190mm (96 x 96 DPI)


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Figure 5: Schematic MO-diagrams for the interactions of (a) an electrophilic radical with CF3X via a three electron bond and (b) of a nucleophilic radical via a one-electron bond. 268x124mm (300 x 300 DPI)



Figure 6: Correlation of log10(-Eint) vs EET. The solid circles and the black dashed regression line are for all complexes with the most favorable EET (i.e. that shown in bold in Table 2). The crosses and the red dashed regression line indicate the data points for the reduced chlorine atom and the green triangles and dashed line those for the oxidized chlorine atom. 254x190mm (96 x 96 DPI)


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Figure 7: 0.001 a.u. isodensity plots of the - (blue) and - (red) MP2/aug-cc-pVTZ spin densities for the complexes of CF3I with CH3, C(CH3)3 and Cl. 338x190mm (96 x 96 DPI)



ToC graphic 79x41mm (300 x 300 DPI)


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The Interaction of Radicals with Ï-Holes

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