Next Article in Journal
A Review on Metal Nanoparticles Nucleation and Growth on/in Graphene
Next Article in Special Issue
σ-Holes on Transition Metal Nanoclusters and Their Influence on the Local Lewis Acidity
Previous Article in Journal
Syntheses, Crystal Structures and Thermal Behaviors of Two Supramolecular Salamo-Type Cobalt(II) and Zinc(II) Complexes
Previous Article in Special Issue
Halogen-Bonded Co-Crystals of Aromatic N-oxides: Polydentate Acceptors for Halogen and Hydrogen Bonds
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

σ-Hole Interactions: Perspectives and Misconceptions

Department of Chemistry, University of New Orleans, New Orleans, LA 70148, USA
*
Author to whom correspondence should be addressed.
Crystals 2017, 7(7), 212; https://doi.org/10.3390/cryst7070212
Submission received: 4 June 2017 / Revised: 21 June 2017 / Accepted: 22 June 2017 / Published: 12 July 2017
(This article belongs to the Special Issue Analysis of Halogen and Other σ-Hole Bonds in Crystals)

Abstract

:
After a brief discussion of the σ-hole concept and the significance of molecular electrostatic potentials in noncovalent interactions, we draw attention to some common misconceptions that are encountered in that context: (1) Since the electrostatic potential reflects the contributions of both the nuclei and the electrons, it cannot be assumed that negative potentials correspond to “electron-rich” regions and positive potentials to “electron-poor” ones; (2) The electrostatic potential in a given region is determined not only by the electrons and nuclei in that region, but also by those in other portions of the molecule, especially neighboring ones; (3) A σ-hole is a region of lower electronic density on the extension of a covalent bond, not an electrostatic potential; (4) Noncovalent interactions are between positive and negative regions, which are not necessarily associated with specific atoms, so that “close contacts” between atoms do not always indicate the actual interactions.

1. A Brief History of the σ-Hole

The σ-hole concept was introduced by Clark in the context of halogen bonding, at a conference in 2005 [1], although it did not appear in the chemical literature until 2007 [2]. Halogen bonding involves a favorable noncovalent interaction between a covalently-bonded halogen and a negative site, such as a lone pair. Such interactions were already known to experimentalists in the 19th century [3,4], and were studied extensively in the 20th [5,6,7,8,9,10], with crystallography playing a major role [10,11,12,13]. Nevertheless the basis for halogen bonding was not really understood. It was frequently rationalized as “charge transfer” from an electron “donor” (e.g., the lone pair) to an “acceptor” (the halogen), invoking the valence bond formalism of Mulliken [14] (which was later put in molecular orbital terms by Flurry [15,16]).
However, the halogen is the most electronegative atom in each row of the periodic table, and a singly-bonded halogen atom is generally viewed as being negative in character. So why should it interact attractively with a donor of electronic charge? It was in fact pointed out long ago [7,17] that Mulliken’s charge-transfer formalism was not intended to be an elucidation of the bonding in a ground-state noncovalent complex; it was purely a mathematical modeling of the transition of the ground-state complex to a low-lying excited state. The existence of halogen bonding was thus viewed by many as an enigma.
The key to resolving the enigma was the molecular electrostatic potential. This is the potential V(r) that is created at any point r in the space of a molecule by its nuclei and electrons, given rigorously by Equation (1):
V ( r ) = A Z A | R A r | ρ ( r ) d r | r r | .
ZA is the charge on nucleus A, located at RA, and ρ(r) is the molecule’s electronic density. Regions in which V(r) is positive, indicating the dominance of the nuclear contribution, are attractive to negative sites; regions of negative V(r) reflect a dominant electronic contribution and are attractive to positive sites.
The electrostatic potential, as given by Equation (1), is a real physical property, and observable. It can be determined experimentally by diffraction techniques [18,19,20] as well as computationally. It is accordingly a physically meaningful representation of the electrostatic effects of the charge distribution in a molecule, unlike calculated atomic charges, which have often been used for the same purpose. These have no physical basis [21,22,23,24]; they are arbitrarily defined by any one of numerous proposed methods and can vary greatly depending upon which method is used. For instance, seven different schemes for assigning atomic charges produced values for the carbon in nitromethane that ranged from −0.478 to +0.564 [23].
What could have been a first step in resolving the enigma of halogen bonding was a study in 1977 by Kollman, who calculated the electrostatic potentials at selected single points around several diatomic molecules [25]. For both F2 and Cl2, he found points with positive potentials to the outsides of the nuclei, on the extensions of the bonds, and points with negative potentials directly above the nuclei, perpendicular to the bonds. He used this observation to explain the fact that the Cl2 dimer does not have the expected T-shaped structure but rather is L-shaped, the positive end of one Cl2 molecule interacting with the negative potential above a nucleus of the other. This is also the orientation of the molecules in the lattice structure of crystalline Cl2 [26,27].
These Cl2---Cl2 interactions are examples of halogen bonding, and Kollman’s points with positive and negative potentials could have been an early clue to its nature. If Mulliken had known about the positive potentials on the outer sides of the halogen atoms, he might not have predicted (incorrectly) that the complex formed between the iodine molecule and benzene has the I2 parallel to the benzene ring [14].
The full explanation of halogen bonding came later, through much more extensive studies by Brinck et al. in which V(r) was computed on the entire molecular surfaces of several molecules containing univalent halogen atoms [28,29], e.g., CH3Br and CCl4. The surfaces were taken to be the 0.001 au contours of the molecular electronic densities, as suggested by Bader et al. [30]; the potential computed on such a surface is labeled VS(r).
It was found that the halogen atoms in these molecules have regions of positive electrostatic potential on their outer sides, on the extensions of their bonds, while their lateral sides are negative. Brinck et al. recognized that these positive regions can interact attractively with negative sites, and thus explain halogen bonding [28,29]. The simultaneous presence of both positive and negative regions also accounts for the observation, in a survey of halide crystal structures [13], that the halogen atoms can interact attractively with negative sites (nucleophiles) along the extensions of their bonds and with positive sites (electrophiles) in lateral directions. In fact it is possible to have a favorable interaction between a positive region on a halogen atom in one molecule and a negative region on the same halogen atom in another, identical molecule [31].
As an example of the positive and negative regions on a univalent halogen atom, Figure 1 shows the electrostatic potential on the 0.001 au surface of the molecule H2PBr, 1. (All calculations to be reported are at the density functional M06-2X/6-31G* level, using the Gaussian 09 [32] and WFA-SAS [33] codes. The 6-31G* basis set has been demonstrated to give reliable electrostatic potentials [34].) In Figure 1a, note the positive potential on the outside of the bromine, along the extension of the P–Br bond; its most positive value (the local VS,max) is 5 kcal/mol. The lateral sides of the bromine are negative.
Crystals 07 00212 i001
What is the origin of such positive potentials on electronegative atoms? It has been known for quite some time that atoms involved in covalent single (and sometimes double) bonds have lesser electronic densities (and shorter radii) on the extensions of the bonds than on their lateral sides [12,26,27,35,36,37,38,39,40]. This has sometimes been called “polar flattening”. For the bromine in Figure 1, the distance from its nucleus to the 0.001 au surface along the extension of the P–Br bond is 2.10 Å, compared to 2.25 Å from the nucleus to a lateral side.
The region of lower electronic density on the extension of a bond is what Clark labeled the σ-hole [2]. Very often there is a positive electrostatic potential associated with it that can interact favorably with a negative site. This is the basis for halogen bonding, as was pointed out by Brinck et al. [28,29].
It is not only covalently-bonded halogens that have lower electronic densities (σ-holes) on the extensions of their bonds; this is true as well of covalently-bonded atoms in other Groups of the periodic table [12,35,36,37,38,40]. In the years 2007–2009, positive σ-hole potentials were found for atoms in Groups VI [41], V [42], and IV [43]. For instance, the phosphorus atom in H2PBr, 1, has three positive σ-hole potentials; the strongest is on the extension of the Br–P bond, Figure 1b, with a maximum value (VS,max) of 33 kcal/mol. Two weaker phosphorus VS,max of 17 kcal/mol are due to the H–P bonds (see Figure 1a,b). The phosphorus also has a negative potential associated with its lone pair.
Just as for the halogens, these positive regions can interact attractively with negative sites, and thus account for noncovalent interactions involving Groups IV–VI that have been known experimentally (and later computationally) for many years [35,37,44,45,46,47,48,49]. However, they were not recognized as σ-hole interactions until 2007−2009 [41,42,43]. Particularly notable was the work of Burling and Goldstein [45], who computed the electrostatic potential in the molecular plane of 1,3-thiazole, 2, and found positive regions on the sulfur that would now be described as positive σ-hole potentials. This explained an intramolecular S---O close contact that stabilizes a biologically active 1,3-thiazole conformation in a nucleoside drug.
Crystals 07 00212 i002
To understand Group IV–VII noncovalent interactions, it is essential to recognize that the electrostatic potentials on the surfaces of covalently-bonded atoms can and frequently do have both positive and negative regions. (Some exceptions that have only positive potentials include atoms linked to very electron-attracting residues and tetravalent Group IV atoms, which have all of their valence electrons in σ bonds.) Atomic charges, whereby each atom is assigned a single positive or negative charge, cannot account for the possibility of simultaneous positive and negative regions.
The interactions that have been discussed are all examples of σ-hole bonding. In recent years, there has developed the unfortunate tendency to label them according to the group: Group IV, tetrel bonding; Group V, pnicogen bonding; Group VI, chalcogen bonding; Group VII, halogen bonding. This obscures the essential point that these are all essentially the same type of interaction.

2. Characteristics of σ-Holes: Some Common Misconceptions

2.1. Locations and Strengths of Positive Potentials

In interpreting molecular electrostatic potentials, it is often assumed that they track the electronic density, i.e., that “electron-rich” regions will have negative potentials and “electron-poor” ones will have positive potentials. While this may sometimes appear to be the case, it cannot, in general, be correct: As Equation (1) shows, and as has been stressed earlier [50,51,52,53,54], the electrostatic potential V(r) at any point r does not reflect only the electronic density at r; V(r) is the resultant of contributions from all of the electrons and all of the nuclei in the molecule. The effect of the nuclei can be very significant. For example, the electrostatic potential of a neutral ground-state atom is positive everywhere despite the electronic charge being exactly equal to the nuclear charge [55]; the effect of the latter dominates over that of the dispersed electrons. It is well established both crystallographically and computationally that the internuclear regions of covalent bonds generally feature buildups of electronic density [20,56,57], yet the electrostatic potentials in bond regions are usually positive [18,50,58]. The contributions of the nuclei prevail. It cannot be assumed that high (low) electronic densities correspond to negative (positive) electrostatic potentials. The potential in a given region is the net result of negative contributions from the electrons and positive ones from the nuclei of the entire molecule, their effects of course being greater as they are closer to the region in question.
A key point in the context of σ-hole interactions is that the term σ-hole refers to a region of lower electronic density along the extension of a covalent bond, not to an electrostatic potential (as is often implied). The lower electronic density (the σ-hole) is usually (not always) reflected in a region of positive potential, but this is subject to influences from other portions of the molecule that frequently affect its magnitude and location [53,54,59].
The situation is most straightforward for halogens. A singly-bonded halogen atom, having only one close neighbor, tends to somewhat protrude from the molecule; note the bromines in H2PBr, 1 (Figure 1) and in 4-bromo-1,2-diazole, 3 (Figure 2). This means that its electrostatic potential is less subject to influences from neighboring atoms, so that the more positive (or less negative) potential due to the σ-hole is typically rather focused along the extension of the bond. In H2PBr, 1, the VS,max of the bromine σ-hole deviates by only 5° from the extension of the P–Br bond; in the diazole 3, the deviation from the extension of the C–Br bond is only 1°. As a result, in a R-X---B complex, where X is a halogen atom and B is the negative site, the angle R-X---B tends to be nearly linear [47,60]; for instance in the complex H2PBr---NCH, 4, which has a calculated interaction energy of −2 kcal/mol, the P-Br---N angle is 174°. (In 4, the phosphorus is yellow, the bromine is red, and the nitrogen is blue.)
Crystals 07 00212 i003
For singly-bonded halogens, the magnitudes of the potentials related to their σ-holes tend qualitatively to become more positive as the remainder of the molecule is more electron-attracting. Thus they depend upon the relative electronegativities and polarizabilities of the halogen and the molecular residue [47,60,61]. This is why crystal engineering through halogen bonding has so frequently involved iodides [62,63]; iodine is the least electronegative and most polarizable halogen, and thus its σ-hole potentials are usually more positive than those of the other halogens. It also explains why fluorine, with its high electronegativity and low polarizability, often has negative potentials associated with its σ-holes, although they are less negative than their surroundings. For example, the fluorines in hexafluorothiacyclobutane, 5 (Figure 3), clearly have σ-holes; the distances to the 0.001 au contour along the bond extensions are 1.55 Å vs. 1.59 Å to their lateral sides. However, the electrostatic potentials on the bond extensions are negative, although less so than on the lateral sides of the fluorines. On the other hand, fluorine does have a positive σ-hole potential when the remainder of the molecule is very strongly electron-attracting [64,65,66], e.g., in FCN.
Crystals 07 00212 i004
For atoms of Groups IV–VI, rationalizing the locations and strengths of electrostatic potentials linked to σ-holes is likely to be more difficult than for the halogens. These atoms can be involved in two or more covalent bonds and the potentials on their surfaces are accordingly more subject to influences from neighbors. Consider the molecule AsFBr(CN), 6 (Figure 4). As would be expected, the arsenic has positive potential regions that can be attributed to σ-holes, with a local VS,max corresponding to each of its three bonds. However, the locations of the VS,max deviate by 19°, 16° and 21° from the extensions of the Br–As, F–As, and NC–As bonds, respectively [54]. In contrast, the VS,max on the bromine deviates by only 4° from the extension of the As–Br bond.
Crystals 07 00212 i005
The interactions of 6 with a negative site roughly follow the locations of these VS,max. In complex 7, which involves a positive region on the extension of the Br–As bond, the angle Br-As---N is 166°. However, in 8, the interaction with the bromine positive region is nearly linear; the angle As-Br---N is 176°. (In 7 and 8, the bromine is red, the arsenic is violet, and the nitrogen is blue.)
Crystals 07 00212 i006
Furthermore, the VS,max on the arsenic are not in accordance with the relative electron-attracting powers of its bond partners. The CN group is much more electron-attracting than either fluorine or bromine [67], yet the arsenic VS,max due to the NC–As bond is the least positive, 37 kcal/mol. Fluorine is more electron-attracting than bromine, but the VS,max due to the F–As and Br–As bonds are the same, 42 kcal/mol. Thus, while there has been some success in relating relative VS,max values to electronegativities and polarizabilities [61,68], we nevertheless echo our earlier statement [61]: “…. in the final analysis the safest approach is to simply compute them.”
On a more positive note, interaction energies do approximately follow the interacting positive and negative potentials, becoming more negative as these potentials are larger in magnitude [47], for Groups IV–VI as well as the halogens. Thus the interaction energies in 7 and 8 are −9 and −3 kcal/mol, respectively, consistent with the VS,max of the positive potentials on the arsenic and the bromine being 42 and 15 kcal/mol.

2.2. Van der Waals Radii and Close Contacts

A widely used criterion for the existence of a noncovalent bond is that the distance between the interacting atoms should be less than or approximately equal to the sum of their van der Waals radii. When this is observed in a crystal lattice for a given pair of atoms, it is called a “close contact” and is taken to indicate an attractive noncovalent interaction.
As has been pointed out, however, there are some problems with this [69,70,71]. One is that van der Waals radii are typically based upon the assumption that the atoms, despite being covalently bonded, are spherical. It is well known that this is not true [12,35,36,37,38,39,40]; σ-holes are in fact a manifestation of the asymmetry of covalently-bonded atoms, which can be quite substantial. From analyses of crystal data, Nyburg and Faerman estimated the radii of chlorines bonded to carbons to be, on the average, 0.2 Å shorter along the extensions of the bonds than perpendicular to them [36]; for sulfurs doubly-bonded to carbons, they found a difference of 0.4 Å. Eramian et al. predict somewhat smaller but still significant asymmetries [40]. How meaningful, then, is it to assign a single radius to the atom?
Another problem is that noncovalent interactions between a given pair of atoms in crystal lattices cover a range of separations; an intermediate one is used in assigning van der Waals radii [69,70,72]. It was pointed out by Dance [69] and by Alvarez [70] that using the sum of van der Waals radii as a criterion is accordingly likely to miss many noncovalent bonds, which can be several tenths of an Angstrom greater than that sum.
This suggests that an internuclear separation less than the sum of the van der Waals radii of the respective atoms should be viewed as a sufficient but not necessary condition for an attractive noncovalent interaction. However, this assumes that the interaction can be attributed to those specific atoms. This is indeed very often the case; crystallography shows numerous examples of close contacts that do indicate noncovalent interactions [12,73]. Similarly, in the complexes 4, 7 and 8 the interactions are specifically between the positive σ-hole potentials of the bromine or arsenic and the negative lone pair of the nitrogen, and their separations (3.22 Å in 4, 2.82 Å in 7 and 3.19 Å in 8) are well below the sums of the respective van der Waals radii (3.52 Å for Br---N and 3.54 Å for As---N [70]).
On the other hand, it is not unusual to find that the most positive (or most negative) potential in a molecular region cannot be associated with a particular atom [53,54,59,73,74,75]. A good example of this is hexafluorothiacyclobutane 5. Given the abundance of highly electronegative fluorines, it is reasonable to expect positive σ-hole potentials on the carbons as well as the sulfur, on the extensions of the bonds to these atoms. Instead, what is found are four positive regions in the plane of the ring (Figure 3), each with a VS,max that is in an intermediate position between the extensions of parallel C–C and C–S bonds. The two VS,max that are between carbons deviate by 19° and 21°, respectively, from the extensions of these bonds, the two that are between a carbon and the sulfur deviate by 22°and 40°. These positive regions cannot be linked to any specific atoms, nor can the resulting interactions with negative sites, as shall be seen.
Two complexes formed between 5 and HCN are shown as structures 9 and 10. In each of these, the lone nitrogen pair is clearly interacting with the strong positive potential that is intermediate between adjacent carbons or a carbon and the sulfur; it is not interacting with any atom individually. The calculated interaction energies are very similar, both about −5 kcal/mol, which is not surprising since the four VS,max range only from 30 to 32 kcal/mol. (In 9 and 10, the sulfurs are yellow, the fluorines are light blue, and the nitrogens are blue. The HCN is slightly tilted in 10, probably due to an attractive interaction between its hydrogen and the nearby fluorines).
Crystals 07 00212 i007
The C---N distances in 9 and the S---N and C---N distances in 10 are all between 2.99 Å and 3.03 Å, so they are considerably less than the sums of the van der Waals radii, 3.43 Å for C---N and 3.55 Å for S---N [70]. Accordingly, these all fit the definition of close contacts; however, they do not correspond to the actual interactions, which are with the intermediate positive potentials.
Analogous situations have been found, both computationally and crystallographically, for a number of other four- and five-membered heterocyclic rings [53,54,59,73]. In each case, the negative site is in close contacts with two neighboring atoms of the ring but the interaction is in reality with the strong positive potential located between the extensions of the bonds to these atoms.
When two atoms with positive σ-hole potentials are in close proximity in a molecule, their positive regions may overlap and result in just a single strong VS,max at some intermediate point rather than two separate ones. The ureas, 11, are a good example of this. Instead of each N–H hydrogen having a σ-hole VS,max, as would be expected, there is just a single one approximately midway between them [73,74]. Thus intermolecular interactions, e.g., in their crystal lattices, that have customarily been described as bifurcated hydrogen bonds, 12 [76,77], are more realistically viewed as in 13. The N–H---O close contacts do not actually correspond to the dominant interactions.
Crystals 07 00212 i008
Overlapping of potentials can also produce another interesting effect, shown for instance by the oxygens in many nitro (NO2) groups. While each oxygen potential does have a minimum (most negative) value at a certain point, these two points are quite close to each other and they are separated by a ridge of essentially the same potentials as the minima (within 1 kcal/mol) [74]. Accordingly the interaction with a positive site, e.g., an amine hydrogen, which is usually described by 14, should actually be regarded as involving this whole ridge of essentially uniform negative potential, as in 15.
Crystals 07 00212 i009

3. Discussion and Summary

Noncovalent interactions are Coulombic in nature. This follows rigorously from the Hellmann–Feynman theorem, in the formulation given by Feynman [78], and it can be seen as well from the fact that the potential energy terms in the Hamiltonian for a noncovalent complex are all Coulombic. The molecular electrostatic potential is accordingly an effective means of analyzing such interactions. However, it is very important to note that the term Coulombic includes the effects of polarization. Some interactions that appear inexplicable in terms of the electrostatic potentials of the ground-state unperturbed molecules become understandable when the polarization is taken into account, i.e., the effect of each molecule’s electric field upon the charge distribution of the other. This has been discussed in detail on a number of occasions [53,54,79,80,81].
In this paper, we have tried to clarify four misconceptions that are often associated with the interpretation of molecular electrostatic potentials:
  • It cannot be assumed that, in general, regions of higher electronic density will have negative electrostatic potentials and that regions of lower electronic density will have positive ones. The electrostatic potential reflects the effects of the nuclei as well as the electrons.
  • A corollary to this is that the electrostatic potential in a given region is not determined only by the electrons and nuclei in that region but also by those in the remainder of the molecule, particularly those in neighboring portions.
  • A σ-hole is a region of lower electronic density on the extension of a covalent bond, not a region of electrostatic potential.
  • Noncovalent interactions are between positive and negative regions, and these may not be associated with specific atoms. Accordingly, close contacts between atoms are not always a reliable indicator of the actual interactions.
These points should be kept in mind in using molecular electrostatic potentials to analyze noncovalent interactions.

Author Contributions

Peter Politzer and Jane S. Murray contributed equally to this manuscript, with Peter Politzer having done most of the writing and Jane S. Murray having carried out the computations.

Conflicts of Interest

The authors declare no conflict of interest.

References

  1. Workshop on Modeling Interactions in Biomolecules II, Prague, 5–9 September 2005. Available online: http://physics.mff.cuni.cz/kchfo/workshop05/ (accessed on 23 June 2017).
  2. Clark, T.; Hennemann, M.; Murray, J.S.; Politzer, P. Halogen bonding: The σ-hole. J. Mol. Model. 2007, 13, 291–296. [Google Scholar] [CrossRef] [PubMed]
  3. Guthrie, F. XXVIII. On the iodide of iodammonium. J. Chem. Soc. 1863, 16, 239–244. [Google Scholar] [CrossRef]
  4. Remsen, I.; Norris, J.F. The action of the halogens on the methylamines. Am. Chem. J. 1896, 18, 90–95. [Google Scholar]
  5. Benesi, H.A.; Hildebrand, J.H. Ultraviolet absorption bands of iodine in aromatic hydrocarbons. J. Am. Chem. Soc. 1948, 70, 2832–2833. [Google Scholar] [CrossRef]
  6. Benesi, H.A.; Hildebrand, J.H. A spectrophotometric investigation of the interaction of iodine with aromatic hydrocarbons. J. Am. Chem. Soc. 1949, 71, 2703–2707. [Google Scholar] [CrossRef]
  7. Slifkin, M.A. Charge Transfer Interactions of Biomolecules; Academic Press: London, UK, 1971. [Google Scholar]
  8. Di Paolo, T.; Sandorfy, C. On the hydrogen bond breaking ability of fluorocarbons containing higher halogens. Can. J. Chem. 1974, 52, 3612–3622. [Google Scholar] [CrossRef]
  9. Dumas, J.-M.; Kern, M.; Janier-Dubry, J.L. Cryoscopic and Calorimetric Study of MX4-Polar Organic Base Interactions (M = C, Si, X = Cl, Br)—Influence of Element and of Halogen. Bull. Soc. Chim. Fr. 1976, 11, 1785–1790. [Google Scholar]
  10. Blackstock, S.C.; Lorand, J.P.; Kochi, J.K. Charge-Transfer Interactions of Amines with Tetrahalomethanes. X-ray Crystal Structures of the Donor-Acceptor Complexes of Quinuclidine and Diazabicyclo[2.2.2]octane with Carbon Tetrabromide. J. Org. Chem. 1987, 52, 1451–1460. [Google Scholar] [CrossRef]
  11. Hassel, O.; Rømming, C. Direct Structural Evidence for Weak Charge Transfer Bonds in Solids Containing Chemically Saturated Molecules. Quart. Rev. Chem. Soc. 1962, 16, 1–18. [Google Scholar] [CrossRef]
  12. Bent, H.A. Structural Chemistry of Donor-Acceptor Interactions. Chem. Rev. 1968, 68, 587–648. [Google Scholar] [CrossRef]
  13. Ramasubbu, N.; Parthasarathy, R.; Murray-Rust, P. Angular Preferences of Intermolecular Forces around Halogen Centers: Preferred Directions of Approach of Electrophiles and Nucleophiles around Carbon-Halogen Bond. J. Am. Chem. Soc. 1986, 108, 4308–4314. [Google Scholar] [CrossRef]
  14. Mulliken, R.S. Molecular Compounds and Their Spectra. II. J. Am. Chem. Soc. 1952, 74, 811–824. [Google Scholar] [CrossRef]
  15. Flurry, R.L., Jr. Molecular Orbital Theory of Electron Donor-Acceptor Complexes. I. A Simple Semiempirical Treatment. J. Phys. Chem. 1969, 69, 1927–1933. [Google Scholar] [CrossRef]
  16. Flurry, R.L., Jr. Molecular Orbital Theory of Electron Donor-Acceptor Complexes. II. Charged Donors and Acceptors. J. Phys. Chem. 1969, 73, 2111–2117. [Google Scholar] [CrossRef]
  17. Dewar, M.J.S.; Thompson, C.C. Π-Molecular complexes—III: A critique for charge-transfer, and stability constants for some TCNE-hydrocarbon complexes. Tetrahedron 1966, 7, 97–114. [Google Scholar] [CrossRef]
  18. Stewart, R.F. On the mapping of electrostatic properties from bragg diffraction data. Chem. Phys. Lett. 1979, 65, 335–342. [Google Scholar] [CrossRef]
  19. Politzer, P.; Truhlar, D.G. (Eds.) Chemical Applications of Atomic and Molecular Electrostatic Potentials; Plenum Press: New York, NY, USA, 1981. [Google Scholar]
  20. Klein, C.L.; Stevens, E.D. Charge Density Studies of Drug Molecules. In Structure and Reactivity; Liebman, J.F., Goldberg, A., Eds.; VCH Publishers: New York, NY, USA, 1988; pp. 26–64. [Google Scholar]
  21. Stone, A.J.; Price, S.L. some new ideas in the theory of intermolecular forces: Anisotropic atom-atom potentials. J. Phys. Chem. 1988, 92, 3325–3335. [Google Scholar] [CrossRef]
  22. Price, S.L. Applications of realistic electrostatic modelling to molecules in complexes, solids and proteins. J. Chem. Soc. Faraday Trans. 1996, 92, 2997–3008. [Google Scholar] [CrossRef]
  23. Wiberg, K.B.; Rablen, P.R. Comparison of atomic charges derived via different procedures. J. Comput. Chem. 1993, 14, 1504–1518. [Google Scholar] [CrossRef]
  24. Murray, J.S.; Politzer, P. The electrostatic potential: An overview. WIREs Comput. Mol. Sci. 2011, 1, 153–163. [Google Scholar] [CrossRef]
  25. Kollman, P. A general analysis of noncovalent intermolecular interactions. J. Am. Chem. Soc. 1977, 99, 4875–4894. [Google Scholar] [CrossRef]
  26. Stevens, E.D. Experimental electron density distributions of molecular chlorine. Mol. Phys. 1979, 37, 27–45. [Google Scholar] [CrossRef]
  27. Tsirelson, V.G.; Zou, P.F.; Tang, T.-H.; Bader, R.F.W. Topological definition of crystal structure determination of the bonded interactions in solid molecular chlorine. Acta Cryst. A 1995, 51, 143–153. [Google Scholar] [CrossRef]
  28. Brinck, T.; Murray, J.S.; Politzer, P. Surface electrostatic potentials of halogenated methanes as indicators of directional intermolecular interactions. Int. J. Quantum Chem. 1992, 44, 57–64. [Google Scholar] [CrossRef]
  29. Brinck, T.; Murray, J.S.; Politzer, P. Molecular electrostatic potentials and local ionization energies of group V–VII hydrides and their anions. Relationships for aqueous and gas-phase acidities. Int. J. Quantum Chem. 1993, 48, 73–88. [Google Scholar] [CrossRef]
  30. Bader, R.F.W.; Carroll, M.T.; Cheeseman, J.R.; Chang, C. Properties of atoms in molecules: Atomic volumes. J. Am. Chem. Soc. 1987, 109, 7968–7979. [Google Scholar] [CrossRef]
  31. Politzer, P.; Murray, J.S.; Concha, M.C. σ-Hole bonding between like atoms. A fallacy of atomic charges. J. Mol. Model. 2008, 14, 659–665. [Google Scholar] [CrossRef] [PubMed]
  32. Frisch, M.J.; Trucks, G.W.; Schlegel, H.B.; Scuseria, G.E.; Robb, M.A.; Cheeseman, J.R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G.A.; et al. Gaussian 09; Revision A.1; Gaussian, Inc.: Wallingford, CT, USA, 2009. [Google Scholar]
  33. Bulat, F.A.; Toro-Labbé, A.; Brinck, T.; Murray, J.S.; Politzer, P. Quantitative analysis of molecular surface properties. J. Mol. Model. 2010, 16, 1679–1691. [Google Scholar] [CrossRef] [PubMed]
  34. Riley, K.E.; Tran, K.; Lane, P.; Murray, J.S.; Politzer, P. Comparative analysis of electrostatic potential maxima and minima on molecular surfaces, as determined by three methods and a variety of basis sets. J. Comput. Sci. 2016, 17, 273–284. [Google Scholar] [CrossRef]
  35. Row, T.N.G.; Parthasarathy, R. Directional preferences of nonbonded atomic contacts with divalent sulfur in terms of its orbital orientations. 2. S---S interactions and nonspherical shape of sulfur in crystals. J. Am. Chem. Soc. 1981, 103, 477–479. [Google Scholar] [CrossRef]
  36. Nyburg, S.C.; Faerman, C.H. A revision of van der waals atomic radii for molecular crystals: N, O, F, S, Cl, Se, Br and I bonded to carbon. Acta Crystallogr. Sect. B Struct. Sci. 1985, 41, 274–279. [Google Scholar] [CrossRef]
  37. Ramasubbu, N.; Parthasarathy, R. Stereochemistry of incipient electrophilic and nucleophilic reactions at divalent selenium center: Electrophilic-nucleophilic pairing and anisotropic shape of Se in Se---Se interactions. Phosphorus Sulfur 1987, 31, 221–229. [Google Scholar] [CrossRef]
  38. Ikuta, S. Anisotropy of electron density distribution around atoms in molecules: N, P, O and S atoms. J. Mol. Struct. (Theochem) 1990, 205, 191–201. [Google Scholar] [CrossRef]
  39. Awwadi, F.F.; Willett, R.D.; Peterson, K.A.; Twamley, B. The nature of halogen-halogen synthons: crystallographic and theoretical studies. Chem. Eur. J. 2006, 12, 8952–8960. [Google Scholar] [CrossRef] [PubMed]
  40. Eramian, H.; Tian, Y.-H.; Fox, Z.; Beneberu, H.Z.; Kertesz, M. On the anisotropy of van der waals atomic radii of O, S, Se, F, Cl, Br, and I. J. Phys. Chem. A 2013, 117, 14184–14190. [Google Scholar] [CrossRef] [PubMed]
  41. Murray, J.S.; Lane, P.; Clark, T.; Politzer, P. σ-Hole bonding: molecules containing group VI atoms. J. Mol. Model. 2007, 13, 1033–1038. [Google Scholar] [CrossRef] [PubMed]
  42. Murray, J.S.; Lane, P.; Politzer, P. A predicted new type of directional noncovalent interaction. Int. J. Quantum Chem. 2007, 107, 2286–2292. [Google Scholar] [CrossRef]
  43. Murray, J.S.; Lane, P.; Politzer, P. Expansion of the σ-hole concept. J. Mol. Model. 2009, 15, 723–729. [Google Scholar] [CrossRef] [PubMed]
  44. Rosenfield, R.E., Jr.; Parthasarathy, R.; Dunitz, J.D. Directional preferences of nonbonded atomic contacts with divalent sulfur. 1. electrophiles and nucleophiles. J. Am. Chem. Soc. 1977, 99, 4860–4862. [Google Scholar] [CrossRef]
  45. Burling, F.T.; Goldstein, B.M. Computational studies of nonbonded sulfur-oxygen and selenium-oxygen interactions in the thiazole and selenazole nucleosides. J. Am. Chem. Soc. 1992, 114, 2313–2320. [Google Scholar] [CrossRef]
  46. Cozzolino, A.F.; Vargas-Baca, I.; Mansour, S.; Mahmoudkhani, A.H. The nature of the supramolecular association of 1,2,5-chalcogenadiazoles. J. Am. Chem. Soc. 2005, 127, 3184–3190. [Google Scholar] [CrossRef] [PubMed]
  47. Politzer, P.; Murray, J.S.; Clark, T. Halogen bonding and other σ-hole interactions: A perspective. Phys. Chem. Chem. Phys. 2013, 15, 11178–11189. [Google Scholar] [CrossRef] [PubMed]
  48. Politzer, P.; Murray, J.S.; Janjić, G.V.; Zarić, S.D. σ-Hole interactions of covalently-bonded nitrogen, phosphorus and arsenic: A survey of crystal structures. Crystals 2014, 4, 12–31. [Google Scholar] [CrossRef]
  49. Bauzá, A.; Mooibroek, T.J.; Frontera, A. The bright future of unconventional σ/π-hole interactions. ChemPhysChem 2015, 16, 2496–2517. [Google Scholar] [CrossRef] [PubMed]
  50. Politzer, P.; Murray, J.S. Molecular Electrostatic Potentials and Chemical Reactivity. In Reviews in Computational Chemistry; Lipkowitz, K.B., Boyd, D.B., Eds.; VCH Publishers: New York, NY, USA, 1991; Volume 2, pp. 273–312. [Google Scholar]
  51. Wheeler, S.E.; Houk, K.N. Through-space effects of substituents dominate molecular electrostatic potentials of substituted arenes. J. Chem. Theory Comput. 2009, 5, 2301–2312. [Google Scholar] [CrossRef] [PubMed]
  52. Murray, J.S.; Shields, Z.P.-I.; Seybold, P.G.; Politzer, P. Intuitive and counterintuitive noncovalent interactions of aromatic π regions with the hydrogen and the nitrogen of HCN. J. Comput. Sci. 2015, 10, 209–216. [Google Scholar] [CrossRef]
  53. Murray, J.S.; Politzer, P. Molecular electrostatic potentials and noncovalent interactions. WIREs Comput. Mol. Sci. 2017, in press. [Google Scholar] [CrossRef]
  54. Politzer, P.; Murray, J.S. σ-Holes and π-Holes: Similarities and differences. J. Comput. Chem. 2017, in press. [Google Scholar] [CrossRef]
  55. Sen, K.D.; Politzer, P. Characteristic features of the electrostatic potentials of singly-negative monoatomic ions. J. Chem. Phys. 1989, 90, 4370–4372. [Google Scholar] [CrossRef]
  56. Coppens, P. Experimental electron densities and chemical bonding. Angew. Chem. Int. Ed. 1977, 16, 32–40. [Google Scholar] [CrossRef]
  57. Feil, D. The electron density distribution in molecular crystals: Exploring the boundary between X-ray diffraction and quantum chemistry. Chem. Scr. 1986, 26, 395–408. [Google Scholar]
  58. Politzer, P.; Daiker, K.C. Models for Chemical Reactivity. In The Force Concept in Chemistry; Deb, B.M., Ed.; Van Nostrand Reinhold: New York, NY, USA, 1981; pp. 294–387. [Google Scholar]
  59. Nayak, S.K.; Kumar, V.; Murray, J.S.; Politzer, P.; Terraneo, G.; Pilati, T.; Metrangolo, P.; Resnati, G. Fluorination promotes chalcogen/tetrel bonding in crystalline solids. CrystEngComm 2017, in press. [Google Scholar] [CrossRef]
  60. Politzer, P.; Murray, J.S. Halogen bonding: An interim discussion. ChemPhysChem 2013, 14, 278–294. [Google Scholar] [CrossRef] [PubMed]
  61. Murray, J.S.; Macaveiu, L.; Politzer, P. Factors affecting the strengths of σ-hole electrostatic potentials. J. Comput. Sci. 2014, 5, 590–596. [Google Scholar] [CrossRef]
  62. Metrangolo, P.; Neukirch, H.; Pilati, T.; Resnati, G. Halogen bonding based recognition processes: A world parallel to hydrogen bonding. Acc. Chem. Res. 2005, 38, 386–395. [Google Scholar] [CrossRef] [PubMed]
  63. Halogen Bonding: Fundamentals and Applications; Metrangolo, P.; Resnati, G. (Eds.) Springer: Berlin, Germany, 2008. [Google Scholar]
  64. Politzer, P.; Murray, J.S.; Concha, M.C. Halogen bonding and the design of new materials: Organic bromides, chlorides and even fluorides as donors. J. Mol. Model. 2007, 13, 643–650. [Google Scholar] [CrossRef] [PubMed]
  65. Chopra, D.; Row, T.N.G. Role of organic fluorine in crystal engineering. CrystEngComm 2011, 13, 2175–2186. [Google Scholar] [CrossRef]
  66. Metrangolo, P.; Murray, J.S.; Pilati, T.; Politzer, P.; Resnati, G.; Terraneo, G. Fluorine-centered halogen bonding: A factor in recognition phenomena and reactivity. Cryst. Growth Des. 2011, 11, 4238–4246. [Google Scholar] [CrossRef]
  67. March, J. Advanced Organic Chemistry, 3rd ed.; Wiley: New York, NY, USA, 1985; p. 247. [Google Scholar]
  68. Bundhun, A.; Ramasami, P.; Murray, J.S.; Politzer, P. Trends in σ-hole strengths and interactions of F3MX molecules (M = C, Si, Ge and X = F, Cl, Br, I). J. Mol. Model. 2013, 19, 2739–2746. [Google Scholar] [CrossRef] [PubMed]
  69. Dance, I. Distance criteria for crystal packing analysis of supramolecular motifs. New J. Chem. 2003, 27, 22–27. [Google Scholar] [CrossRef]
  70. Alvarez, S. A cartography of the van der waals territories. Dalton Trans. 2013, 42, 8617–8636. [Google Scholar] [CrossRef] [PubMed]
  71. Murray, J.S.; Politzer, P. In search of the “impenetrable” volume of a molecule in a noncovalent complex. Mol. Phys. 2017, in press. [Google Scholar]
  72. Rowland, R.S.; Taylor, R. Intermolecular nonbonded contact distances in organic crystal structures: Comparison with distances expected from van der waals radii. J. Phys. Chem. 1996, 100, 7384–7391. [Google Scholar] [CrossRef]
  73. Politzer, P.; Resnati, G.; Murray, J.S. Close contacts and noncovalent interactions in crystals. Faraday Disc. 2017. [Google Scholar] [CrossRef]
  74. Politzer, P.; Murray, J.S. Quantitative analyses of molecular surface electrostatic potentials in relation to hydrogen bonding and Co-crystallization. Cryst. Growth Des. 2015, 15, 3767–3774. [Google Scholar] [CrossRef]
  75. Cavallo, G.; Murray, J.S.; Politzer, P.; Pilati, T.; Ursini, M.; Resnati, G. Halogen bonding in hypervalent iodine and bromine derivatives: Halonium salts. IUCrJ 2017, 4, 411–419. [Google Scholar] [CrossRef]
  76. Etter, M.C.; Urbanczyk-Lipkowska, Z.; Zia-Ebrahimi, M.; Panunto, T.W. Hydrogen bond directed cocrystallization and molecular recognition properties of diarylureas. J. Am. Chem. Soc. 1990, 112, 8415–8426. [Google Scholar] [CrossRef]
  77. Näther, C.; Döring, C.; Jess, I.; Jones, P.G.; Taouss, C. Thermodynamic and structural relationships between the two polymorphs of 1,3-dimethylurea. Acta Crystallogr. Sect. B Struct. Sci. 2013, 69, 70–76. [Google Scholar] [CrossRef]
  78. Feynman, R.P. Forces in molecules. Phys. Rev. 1939, 56, 340–343. [Google Scholar] [CrossRef]
  79. Politzer, P.; Murray, J.S.; Clark, T. σ-Hole bonding: A physical interpretation. Top. Curr. Chem. 2015, 358, 19–42. [Google Scholar] [PubMed]
  80. Clark, T.; Politzer, P.; Murray, J.S. Correct electrostatic treatment of noncovalent interactions: The importance of polarisation. WIREs Comput. Mol. Sci. 2015, 5, 169–177. [Google Scholar] [CrossRef]
  81. Politzer, P.; Murray, J.S.; Clark, T. Mathematical modeling and physical reality in noncovalent interactions. J. Mol. Model. 2015, 21, 52. [Google Scholar] [CrossRef] [PubMed]
Figure 1. Computed electrostatic potential on the 0.001 au molecular surface of H2PBr, 1. In (a), the bromine is in the foreground, to the left. In (b), it is in the rear, to the left. Color ranges, in kcal/mol: red, greater than 16; yellow, between 16 and 8; green, between 8 and 0; blue, less than 0 (negative). The black hemispheres show the locations of the most positive potentials, the VS,max. In (a) is shown the VS,max on the bromine and one of the three on the phosphorus; In (b) are shown the other two VS,max on the phosphorus. The hydrogens do not have separate VS,max in this molecule.
Figure 1. Computed electrostatic potential on the 0.001 au molecular surface of H2PBr, 1. In (a), the bromine is in the foreground, to the left. In (b), it is in the rear, to the left. Color ranges, in kcal/mol: red, greater than 16; yellow, between 16 and 8; green, between 8 and 0; blue, less than 0 (negative). The black hemispheres show the locations of the most positive potentials, the VS,max. In (a) is shown the VS,max on the bromine and one of the three on the phosphorus; In (b) are shown the other two VS,max on the phosphorus. The hydrogens do not have separate VS,max in this molecule.
Crystals 07 00212 g001
Figure 2. Computed electrostatic potential on the 0.001 au molecular surface of 4-bromo-1,2-diazole, 3. The atom positions are as in structure 3, the bromine being at the lower left. Color ranges, in kcal/mol: red, greater than 16; yellow, between 16 and 8; green, between 8 and 0; blue, less than 0 (negative). The black hemispheres show the locations of the most positive potentials, the VS,max, one on the bromine, and one on each hydrogen.
Figure 2. Computed electrostatic potential on the 0.001 au molecular surface of 4-bromo-1,2-diazole, 3. The atom positions are as in structure 3, the bromine being at the lower left. Color ranges, in kcal/mol: red, greater than 16; yellow, between 16 and 8; green, between 8 and 0; blue, less than 0 (negative). The black hemispheres show the locations of the most positive potentials, the VS,max, one on the bromine, and one on each hydrogen.
Crystals 07 00212 g002
Figure 3. Computed electrostatic potential on the 0.001 au molecular surface of hexafluorothiacyclobutane, 5. In (a), the sulfur is in the foreground, with CF2 groups behind it on both sides. In (b), a CF2 group is in the foreground, the other two being behind it on both sides; the sulfur is in the rear, not visible. In (c), the view is from above the four-membered ring.
Figure 3. Computed electrostatic potential on the 0.001 au molecular surface of hexafluorothiacyclobutane, 5. In (a), the sulfur is in the foreground, with CF2 groups behind it on both sides. In (b), a CF2 group is in the foreground, the other two being behind it on both sides; the sulfur is in the rear, not visible. In (c), the view is from above the four-membered ring.
Crystals 07 00212 g003
Figure 4. Computed electrostatic potential on the 0.001 au molecular surface of AsFBr(CN), 6. In (a), the arsenic is in the foreground, the bromine is to the lower left and the CN is to the lower right. In (b), the fluorine is in the foreground to the left, the bromine is in the foreground to the right and the CN is at the top. Color ranges, in kcal/mol: red, greater than 30; yellow, between 30 and 15; green, between 15 and 0; blue, less than 0 (negative). The black hemispheres show the locations of the locally most positive potentials, the VS,max. In (a) can be seen the three VS,max on the arsenic, and in (b) the one on the bromine.
Figure 4. Computed electrostatic potential on the 0.001 au molecular surface of AsFBr(CN), 6. In (a), the arsenic is in the foreground, the bromine is to the lower left and the CN is to the lower right. In (b), the fluorine is in the foreground to the left, the bromine is in the foreground to the right and the CN is at the top. Color ranges, in kcal/mol: red, greater than 30; yellow, between 30 and 15; green, between 15 and 0; blue, less than 0 (negative). The black hemispheres show the locations of the locally most positive potentials, the VS,max. In (a) can be seen the three VS,max on the arsenic, and in (b) the one on the bromine.
Crystals 07 00212 g004

Share and Cite

MDPI and ACS Style

Politzer, P.; Murray, J.S. σ-Hole Interactions: Perspectives and Misconceptions. Crystals 2017, 7, 212. https://doi.org/10.3390/cryst7070212

AMA Style

Politzer P, Murray JS. σ-Hole Interactions: Perspectives and Misconceptions. Crystals. 2017; 7(7):212. https://doi.org/10.3390/cryst7070212

Chicago/Turabian Style

Politzer, Peter, and Jane S. Murray. 2017. "σ-Hole Interactions: Perspectives and Misconceptions" Crystals 7, no. 7: 212. https://doi.org/10.3390/cryst7070212

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop