# What is charge shift bonding?

Can someone explain to me charge shift bonding? I recognize that it is proposed as another domain of bonding - one different from ionic and covalent bonding. I am also told that $\ce{C-F}$ exhibits charge shift bonding. But why—and firstly, what exactly is charge shift bonding? All the literature I have consulted are at too high of a level for me, for example this 1992 article in the Journal of the American Chemical Society.

OK, this was a new one to me too, but I found a few resources which might be useful:

The basic idea is this. Most bonds are ionic (i.e., both atoms are charged, but electrostatically attracted) or covalent (i.e., the electron pair is shared).

(This is largely cribbed from the Comp. Org. Chem. blog post. Thanks to Steven Bachrach)

If we were writing a multi-configurational wavefunction to describe the bond, we might have something like:

$$\psi(\mathrm{VB}) = c_1\psi_\mathrm{covalent} + c_2\psi_{\ce{A+B-}} + c_3\psi_{\ce{A-B+}}$$

So normally, we'd look at which is the dominant configuration - maybe it's the covalent one ($c_1$) or one of the ionic ones ($c_2$ or $c_3$). Instead, sometimes the covalent form isn't even stabilizing!

From my perspective, the classic example given for this charge-shift bond is $\ce{F2}$ which of course has many $\pi^*$ anti-bonding electrons, so the classical bond order is 1, but ignores that there's a lot of antibonding character. But you can't really consider $\ce{F2}$ an ionic compound!

I think the big question is the future - can this new type of bonding show general predictability and utility. Clearly most chemists have a general intuition (if sometimes wrong) of covalent and ionic bonding. Besides the authors, I'm not sure if anyone else has an intuition of charge-shift systems.

• Would a classical explanation of the instability of F2 involve lone pair-lone pair repulsions? – Dissenter Sep 13 '14 at 22:20
• IIRC, that's the Lewis-style explanation. I think the question is if there is so much LP-LP repulsion (i.e., six lone pairs!) why is there a bond? – Geoff Hutchison Sep 13 '14 at 22:26
• Is there lp/lp repulsion in diatomic nitrogen as well? – Dissenter Sep 13 '14 at 22:47
• I am not a VB expert. I'd answer from the MO perspective, which would say such effects are minimal. $N_2$ is, after all, a very strong bond, without anti bonding $\pi$ character. – Geoff Hutchison Sep 14 '14 at 16:24

Geoff has summarized well the mathematical, VB wavefunction-based description of charge-shift bonding. This answer aims to provide further exposition, from the perspective of the distribution of the electron density and of the electron localization in charge-shift bonded as compared to traditional covalent systems. Much of my understanding and argumentation is derived from the Shaik/Hiberty Nature Chemistry review that Geoff linked to, but I also have read through a variety of other papers on the subject (a list of much of the literature I've turned up thus far is provided at the end of the answer).

Please bear in mind that I'm no particular expert in this topic, but am just summarizing my current understanding based upon what I've read to date. Please also bear in mind that this description is at times intentionally qualitative/descriptive, rather than technically precise. Due to both of these aspects, I welcome any corrections/improvements.

The first thing to grasp in understanding charge-shift bonding is the difference between the electron density at a point and the electron localization at a point. The electron density is pretty straightforward, representing the 'concentration' of electrons at each point in space. Electron localization is more subtle, and effectively represents the extent to which the electrons contributing to the density at a given point in space also "visit" other points in the system as they go about their statistical quantum-mechanical wavefunction-y meanderings. In particular, it's critical to understand that the density and the localization are not rigorously correlated: the localization can be low even when the density is high, and vice versa.

One of the most common metrics I've seen for localization is the electron localization function (ELF), which uses the Pauli exclusion behavior of electrons to define their extent of localization on a scale from zero to one. At a high level, this exclusion behavior means that wherever in space a particular reference electron "visits" in the statistical quantum-mechanical sense, the exclusion principle requires that the likelihood of finding a different electron of the same spin in that spatial region must be correspondingly reduced. This distribution of the decreased likelihood of finding another electron due to the statistical "visiting" of a reference electron is called the Fermi hole for that reference electron. So, if the aggregate Fermi hole associated with the electron density at a given point is compact and close to that point, the ELF will be high there (close to unity). Conversely, if the Fermi hole is diffuse and spread far from the reference point, then the ELF will be lower.

The second thing to grasp in understanding charge-shift bonding is the phenomenon of Pauli repulsion, also called 'exchange repulsion,' which is a truly weird, quantum-mechanics-only thing. In this case, if the wavefunction for a system "tries to push too many electrons too close together," Pauli repulsion causes them to delocalize away from the region where they're "too compressed." In other words, the "compressed" electrons will in general end up "visiting" a much larger region of space than they would if fewer electrons were being squeezed into the area of interest. Again, as noted above, this delocalization doesn't necessarily mean that the electron density will decrease appreciably in the Pauli-repulsed region—in many cases the density will remain relatively high even as the localization drops precipitously.

Ok, so: on to charge-shift bonding. If the localization of the electron distribution for a particular bond were a balloon and Pauli repulsion were an adorable puppy, charge-shift bonding is basically this:

In situations where a molecule "tries to cram too many electrons into a bonding region," the bonding electrons "rebel" and flee (delocalize) to other regions of the molecule. The most straightforward way to describe this behavior in a wavefunction is via the valence bond-type mixed covalent/ionic approach presented by Geoff, and is indeed the way Shaik and Hiberty cast it in the Nature Chemistry review. To use the same $\ce{F2}$ example as Geoff, the charge-shift bonding in molecular fluorine can be represented as a resonance:

$$\def\splrar{\enspace \longleftrightarrow \enspace} \ce{F+\!\cdots F^- \!\splrar F-F \splrar F^-\!\cdots F^+}$$

Just like the six-fold-symmetric electron distribution of benzene can be thought of as a resonant superposition of two structures with discrete, alternating double and single bonds, the electronic structure of molecular fluorine can be thought of as a resonant superposition of covalent and ionic electronic configurations. The two ionic resonance structures provide the 'space' for the 'fleeing electrons' to delocalize into, pushed out from the bonding region by Pauli repulsion. In this case, since $\ce{F2}$ is symmetrical about the bond, the contributions of the two ionic resonance structures are necessarily equal; this will not always be the case in general.

In order to demonstrate the nature of charge-shift bonding more explicitly, I'll show the results of a QTAIM and ELF analysis of the isoelectronic series $\ce{A2H_x}~\left(\ce{A} = \ce{\{C,N,O,F\}},~x=\{6,4,2,0\}\right)$, which is one of the prototypical examples of the spectrum between covalent and charge-shift bonding as described by Shaik and Hiberty.

I ran DFT geometry optimizations on each of the four species with ORCA v3.0.3, with input files like the following:

! UKS PBE0 def2-TZVP def2-TZVP/J RIJCOSX
! GRID5 GRIDX8 TIGHTOPT
! ANFREQ

* xyzfile 0 1 C2H6_init.xyz


The initial geometries were created in Avogadro, and I included the frequency calculation to confirm that I'd obtained minimum-energy geometries (probably overkill for such simple systems, but it never hurts to check). I then used the ORCA tool orca_2mkl to generate MOLDEN files for import into MultiWFN v3.3.7 for QTAIM topology and ELF basin analyses, and for electron density and ELF contour plots.

The following figure shows electron density contour plots for the four species (click any of the below figures for the full size version):

For clarity, I've intentionally plotted a comparatively small number of contour lines. I'm pretty sure the scale in each figure is the same, so visual inspection of the contours should give a reliable sense of their relative sizes. For emphasis, I've bolded the $0.2$ contour; while the various hydrogens and lone pairs obscure things somewhat on the periphery of the molecules, the electron density in the area between the two heavy atoms in each system (viz., in the bonding region) really doesn't change all that much in going from $\ce C$ to $\ce F$. The electron density does increase somewhat in the vicinity of each heavy atom along the series (the increase in the diameter of the $1.0$ contour is the most visible indicator of this), which nicely correlates with the increase in electronegativity / nuclear charge.

This relatively modest change in the bonding electron density along the series stands in stark contrast to the trend in electron localization in the bonding region, as illustrated by ELF contour plots of the four species:

Again, for clarity I've intentionally only plotted a few contour lines, and again I've bolded one contour $(0.7)$ for emphasis. Here the differences in going down the series are stark: the localization in the $\ce{C\! -\! C}$ bonding region is large and strong, peaking well above $0.8$. The $\ce{N\! -\! N}$ bond localization is relatively strong but noticeably reduced, whereas in $\ce{H2O2}$ the $\ce{O\! -\! O}$ bond localization has fallen to the point that it doesn't even have an $0.8$ contour line. $\ce{F\! -\! F}$ is even more dramatic, as the bond region doesn't even have an ELF contour line at $0.7$. The ELF basins as calculated by MultiWFN show the same decreasing trend in terms of size going down the series:

In the above, the clusters of dark green dots mark the ELF basins for the bonding regions, while the light green dots mark ELF attractors for lone pairs. The fluorine atoms in $\ce{F2}$ have "rings" of degenerate lone pair attractors since there are no hydrogen nuclei present to 'lock down' the positions of the lone pair attractors, in contrast to $\ce{H2O2}$ and $\ce{N2H4}$.

Both QTAIM analysis at the line critical points (LCPs, called bond critical points by Bader) between the two heavy atoms, as well as population/localization analysis within the ELF bonding basins, reveal illustrative trends (or the lack thereof) within this series of molecules:

$$\begin{array}{ccccccc} \hline ~ & ~ & \text{Units} & \ce{C2H6} & \ce{N2H4} & \ce{H2O2} & \ce{F2} \\ \hline ~ & \rho & {\mathrm{e}^- \over \mathrm{Bohr}^3} & 0.247 & 0.317 & 0.300 & 0.316 \\ \text{Bond LCP} & \nabla^2\rho & {\mathrm{e}^- \over \mathrm{Bohr}^5} & -0.617 & -0.609 & -0.012 & 0.514 \\ ~ & \mathrm{ELF} & {\small (unitless)} & 0.956 & 0.895 & 0.769 & 0.647 \\ \hline ~ & \iiint{\rho} & \mathrm{e}^- & 1.816 & 1.346 & 0.608 & 0.249 \\ \text{ELF Basin} & \text{Volume} & \mathrm{Bohr}^3 & 17.65 & 7.02 & 2.33 & 0.76 \\ ~ & \text{%LI} & {\small (unitless)} & 46.5\% & 37.1\% & 20.4\% & 9.6\% \\ \hline \text{Shaik %CS} & ~ & {\small (unitless)} & 30.2\% & 65.7\% & 114.3\% & 183.9\% \\ \hline \end{array}$$

The "Shaik %CS" values represent the fraction of the bond energy provided by the charge-shift character of each bond as reported in the Nature Chemistry review, in this case with the remainder provided by the "pure" covalent electronic structure for the system. Thus, for $\ce{C2H6}$, $30.2\%$ of the bond energy derives from charge-shift behavior, while $69.8\%$ is due to the covalent contribution. As can be seen, it is possible for this value to be greater than $100\%$, in which case the purely covalent structure would be unbound. The experimentally observed stability of $\ce{H2O2}$ and $\ce{F2}$ is thus due entirely to the charge-shift phenomenon.

Consistent with the contour plots, there is minimal change in the LCP electron density through the series, whereas both (a) the ELF at the bond LCP and (b) the fraction of electrons localized within the ELF bonding basin $(\text{%LI})$ drop significantly in going from $\ce{C2H6}$ to $\ce{F2}$. There is a reasonably significant (albeit nonlinear) trend in the Laplacian of the density ($\nabla^2\rho$), but it appears to be a quirk of the homodiatomic nature of the systems: Shaik and Hiberty have found heteroatomic systems with significant charge-shift character that still show a negative value for the Laplacian at the bond LCP. To emphasize: the sign of the Laplacian is not a reliable diagnostic of charge-shift character!

The ELF basin populations show the same drop along the series, though this is due more than anything to the precipitous decrease in the sizes of the ELF bond basins (recall that the electron density in the bonding region changes very little among the systems).

In summary, charge-shift bonding occurs when the molecular structure requires a sufficient number of electrons to reside in the bonding region of interest to result in substantial delocalization of those electrons away from that bonding region, driven by the effects of Pauli repulsion. Per the Shaik & Hiberty Nature Chemistry review, systems where charge-shift bonding is expected to occur include: small, lone-pair rich, and/or electronegative atoms; $\pi$-bonds in doubly and triply bonded molecules; hypercoordinated compounds (oxoanions, $\ce{IF_x}$, etc.); compact cations with charge strongly localized on a single nucleus (e.g., $\ce{(CH3)3Si^+}$); and, potentially, certain organometallic and/or metal-metal bonds.

Selected Literature $\require{begingroup}\begingroup$

This list includes all of the papers I could find by Hiberty and/or Shaik that pertain to charge-shift bonding, as well as a few I've come across written by other authors.

Papers I would regard as core reading are marked with '$\def\bp{\mathbf +}\bp$'.

Papers not authored by Shaik or Hiberty are marked with '$\def\bt{\mathbf \times}\bt$'.

• "Covalent, ionic and resonating single bonds." J Mol Struct (Theochem) 229: 163 (1991) – doi:10.1016/0166-1280(91)90144-9

• "The charge-shift bonding concept. Electron-pair bonds with very large ionic-covalent resonance energies." J Am Chem Soc 114: 7861 (1992) – doi:10.1021/ja00046a035 $\bp$

• "The non-linear tendencies in homonuclear $\ce{X-X}$ bonds $(\ce{X = Li\text{ to }F})$ and the lone-pair bond weakening effect. An ab initio theoretical analysis." J Mol Struct (Theochem) 338: 283 (1995) – doi:10.1016/0166-1280(94)04067-3

• "Comparison of $\ce{C−Cl}$ and $\ce{Si−Cl}$ Bonds. A Valence Bond Study." J Phys Chem 100: 5715 (1996) – doi:10.1021/jp960145l

• "Charge-Shift Bonding in Group IVB Halides: A Valence Bond Study of $\ce{MH3−Cl (M = C, Si, Ge, Sn, Pb)}$ Molecules." J Am Chem Soc 121: 822 (1999) – doi:10.1021/ja982218f – Erratum: doi:10.1021/ja995530d

• "$\pi$ Bonding in Second and Third Row Molecules: Testing the Strength of Linus's Blanket." Chem Eur J 6(13): 2425 (2000) – doi:10.1002/1521-3765(20000703)6:13<2425::AID-CHEM2425>3.0.CO;2-0

• "Charge-Shift Bonding—A Class of Electron-Pair Bonds That Emerges from Valence Bond Theory and Is Supported by the Electron Localization Function Approach." Chem Eur J 11: 6358 (2005) – doi:10.1002/chem.200500265

• "Barriers of hydrogen abstraction vs halogen exchange: An experimental manifestation of charge-shift bonding." J Am Chem Soc 128(9): 2836 (2006) – doi:10.1021/ja053130m

• "The physical origin of large covalent-ionic resonance energies in some two-electron bonds." Faraday Discussions 135: 261 (2007) – doi:10.1039/b605161h $\bp$

• "Heterolytic bond dissociation in water: Why is it so easy for $\ce{C4H9Cl}$ but not for $\ce{C3H9SiCl}$?" J Phys Chem A 112(13): 2988 (2008) – doi:10.1021/jp8004647

• "Charge-shift bonding and its manifestations in chemistry." Nature Chemistry 1: 443 (2009) – doi:10.1038/nchem.327 $\bp$

• "An Excursion from Normal to Inverted $\ce{C-C}$ Bonds Shows a Clear Demarcation between Covalent and Charge-Shift $\ce{C-C}$ Bonds." ChemPhysChem 10: 2658 (2009) – doi:10.1002/cphc.200900633

• "The electronic structure of the $\ce{F2}$, $\ce{Cl2}$, $\ce{Br2}$ molecules: the description of charge-shift bonding within the generalized valence bond ansatz." Theor Chem Acc 122(1-2): 51 (2009) – doi:10.1007/s00214-008-0484-x $\bt$

• "Topology of Electron Charge Density for Chemical Bonds from Valence Bond Theory: A Probe of Bonding Types." Chem Eur J 15(12): 2979 (2009) – doi:10.1002/chem.200802134

• "Halogen Bonding: A Study based on the Electronic Charge Density." J Phys Chem A 114: 552 (2010) – doi:10.1021/jp907550k $\bt$

• "The Nature of the Idealized Triple Bonds Between Principal Elements and the sigma Origins of Trans-Bent Geometries-A Valence Bond Study." J Chem Theor Comput 7(4): 955 (2011) – doi:10.1021/ct100741b

• "The mechanics of charge-shift bonds: A perspective from the electronic stress tensor." Chem Phys Lett 510: 18 (2011) – doi:10.1016/j.cplett.2011.05.023 $\bt$

• "An MO-Based Identification of Charge-Shift Bonds." ChemPhysChem 13: 2377 (2012) – doi:10.1002/cphc.201200147 $\bt$

• "The essential role of charge-shift bonding in hypervalent prototype $\ce{XeF2}$." Nature Chem 5(5): 417 (2013) – doi:10.1038/nchem.1619

• "Charge-Shift Bonding Emerges as a Distinct Electron-Pair Bonding Family from Both Valence Bond and Molecular Orbital Theories." J Chem Theor Comput 10: 2410 (2014) – doi:10.1021/ct500367s $\bp$

• "A Valence Bond Model for Electron-Rich Hypervalent Species: Application to $\ce{SF_n}$ $(n=1, 2, 4)$, $\ce{PF5}$, and $\ce{ClF3}$." Chem Eur J 20(31): 9643 (2014) – doi:10.1002/chem.201402755

• "Protonated Alcohols Are Examples of Complete Charge-Shift Bonds." J Org Chem 79(21): 9998 (2014) – doi:10.1021/jo501549q

• "More insight in multiple bonding with valence bond theory." Comput Theor Chem 1053(SI): 180 (2015) – doi:10.1016/j.comptc.2014.09.007 $\bp$

• "The Nature of Bonding in Metal-Metal Singly Bonded coinage metal dimers: $\ce{Cu2}$, $\ce{Ag2}$ and $\ce{Au2}$." Comput Theor Chem, in press doi:10.1016/j.comptc.2017.02.013

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I think the two answers currently here are excellent, very detailed and a great read. I thought I would give a different perspective on charge-shift bonding, from the view of the virial theorem.

The weakness of the $\ce{F-F}$ bond in difluorine, $\ce{F2}$, is usually attributed to the lone pair bond weakening effect (LPBWE). This is classically seen as the lone pairs on $\ce{F2}$ repelling the bonding electrons, and so weakening the bond. In MO theory it is attributed to the antibonding effect of filling two antibonding π orbitals. It can also been seen in a different light, that of the balance of kinetic energy ($T$) and potential energy ($V$).

Usually when a covalent bond forms, there are 2 "phases" of bonding. Consider $\ce{H2}$. At infinite separation there is no overlap of the H 1s orbitals. Alternatively, there is no probability of the H 1s electrons tunneling from one nucleus' potential well to the other H atom's potential well. When the H atoms are brought to a finite distance apart, there becomes a finite probability of the H 1s electrons tunneling from one nucleus' potential well to the other. This means that each electron is more spread out - i.e. it occupies a larger volume. This can been seen as making the wavefunction more diffuse, less steeply varying, and so the curvature and Laplacian of the wavefunction takes smaller values. This means the kinetic energy of the electron is consequently smaller - a smaller Laplacian at all distances, averages to give an expectation kinetic energy which is also smaller. This is the primary mode of bonding interaction at long distances - a decrease in kinetic energy.

At around two times the equilibrium bond length $\ce{r0}$, the kinetic energy reaches a minimum (this is for the case of $\ce{H2}$, not generally). This puts the kinetic energy ($T$) and potential energy ($V$) out of balance:

$$\frac{\langle T \rangle}{-\langle V \rangle} < \frac{1}{2}$$

This is the virial theorem, stated for equilibrium bond lengths. The next "phase" which occurs is orbital shrinking - this lowers the potential energy term, and also increases the kinetic energy term, and so restores the balance between the two terms. Thus by the time the equilibrium bond distance is achieved the kinetic energy term is positive, and the potential energy term is twice as negative, leading to an overall binding energy:

$$E = T + V$$

Turning to the case of $\ce{F2}$, let's consider this orbital shrinkage. Due to the presence of lone pairs, Pauli repulsion - where 2 electrons of the same spin can't occupy the same space - brings an additional rise in kinetic energy. This can mean that instead of a deficit of kinetic energy, there is a surplus of kinetic energy. The most extreme example is difluorine, $\ce{F2}$, which doesn't have a covalent minimum - the lone pairs simply repel each other too much, and cancel out any decrease in kinetic energy which may occur due to usual covalent mechanism, of tunneling from one nucleus to the other.

This gives us all we need to understand the phenomena of charge-shift bonding. When bonding was first considered, a supposition of wavefunctions was assumed:

$$\psi_{\mathrm{VB}} = \psi_{\ce{A-B}} + \psi_{\ce{A+B-}} + \psi_{\ce{A^-B+}}$$

The first term is the covalent wavefunction, and the second and third are the ionic contributions. In terms of energy levels and resonance energies we get:

On the left we have the situation for a mostly covalent bond, and on the left the situation for a mostly ionic bond.

Pauling's assumption was that the resonance energy between the covalent and ionic structures was very small, and so proceeded to calculate based on the assumption the $RE_{CS}$ was zero. His second assumption was that the covalent structure was always a binding structure.

Taking again the structure of $\ce{F2}$ the covalent structure is non-bonding at all distances. However by adding in ionic contributions: $\ce{F+ F- <-> F- F+}$ with the covalent structure, a large $RE_{CS}$ is generated providing the binding energy.

Now what do these ionic structures mean? To tie into the excellent answers above, based on electron localisation functions (ELF), we can think of these ionic structures as representing the large electron fluctuation away from the binding region. These ionic structures therefore give a lowering in kinetic energy, with little effect on the potential energy - Precisely what is needed to correct the surplus of kinetic energy caused by LPBWE. In difluorine this effect accounts for the binding interaction completely. Down 1 period, $\ce{Cl2}$ this accounts for a shortening and strengthening of the bond. To tie in with the above idea of orbitals typically contracting during covalent bonding, we find that for $\ce{H2}$, $\ce{H3C-CH3}$, $\ce{H2N-NH2}$ we find significant contraction of the orbitals - IE a covalent interaction. In $\ce{H2O2}$ and $\ce{F2}$, $\ce{Cl2}$, for the purely covalent structures, the orbitals actually increase in size, due the LPBWE. However when we add in the ionic structures, we find that in all cases the orbitals have contracted to some extent. In the case of CS bonds - $\ce{H2O2}$ ,$\ce{F2}$ and $\ce{Cl2}$ - this occurs because the addition of ionic structures negates the increase in KE due to the LPBWE, and so allows for a small degree of orbital shrinking to take place. Before adding in ionic structures, orbitals actually grow, in an attempt to decrease KE by delocalisation.

This picture also ties in with the ELF diagrams shown in other answers. Difluorine looks as if the fluorine atoms have a very much "closed shell" interaction" - the disynaptic region is depleted, with minimal electron density, and a large electron fluctuation away from the site. This matches with the "closed shell" ionic structures, in which there is no "sharing" of electrons.

In summary, charge shift bonding can be seen to stem from the LPBWE whereby lone pairs excessively raise the kinetic energy. In this case the normal mechanism of covalent bond forming - orbital shrinkage - is no longer appropriate. In order to restore the balance of kinetic and potential energy, it is necessary to add in ionic structures, in a VB approach, which represent the electrons becoming more delocalised/less localised, away from the bonding site, thereby lowering the kinetic energy. Once this has happened, orbital shrinkage can occur to a small extent. In this way charge shift bonding can be characterized by small, electron rich fragments, typically electronegative - Eg. Halogens, peroxides, with minimal electron density in the binding region, and electrons which are localised only to a small extent - Pauli repulsion "pushes" them away, the ionic structures "providing space" in a sense for this to occur. Obviously the ionic structures are simply resonance forms - what they describe is the delocalisation of electron density away from the binding sites, resulting in a decrease in kinetic energy, and so restoring the balance of kinetic and potential energy dictated by the virial theorem.