# Delta Bond Or Pi Bond, Which Is More Strong? [closed]

It is pretty evident that sigma bonds are more stronger than pi bonds. (due to the extent of overlapping)

But when there are 4 lobes of two d-orbitals involved in overlapping as that is the case in formation of 'delta bond', is it more stronger than pi bond ?

[it would of great help, if you can list down the sources backing your answers too]

• Usually stronger .... $\ce{N-N}\ \pu{160 kJ/mol}$ // $\ce{N=N}\ \pu{418 kJ/mol}$ // $\ce{N#N}\ \pu{941 kJ/mol}$ Jun 27, 2023 at 19:18
• can you kindly elaborate it a bit ? Jun 27, 2023 at 19:56
• Can you kindly elaborate a bit what I could kindly elaborate a bit? // 1 sigma bond with 2 pi bonds is almost 6 times stronger than just 1 sigma bond. Jun 27, 2023 at 20:20
• mate, the initial question speaks about the comparision between pi and delta bond. You did not compare the so anywhere in the solution. Jun 27, 2023 at 20:28
• Comments are not supposed to answer the question, otherwise they would be posted as answers. Jun 27, 2023 at 20:34

In the case of transition elements, these bonds are involved in the transition from an isolated atom to a transition metal solid. A simple approach for understanding this transition by keeping an intuitive description is to use atomic orbitals, precisely a linear combination of atomic orbitals (LCAO) basis set of the Tight-binding approximation. A useful picture summarizing this approximation is this Hamiltonian : $$\hat{H} = - t \sum_{i,j,\sigma} c_{j \sigma}^\dagger c_{i \sigma} + h.c$$. which means that an electron can hop from an atomic site $$i$$ to another atomic site $$j$$ with a transfer integral $$t$$ as the strength of this motion leadind a bandstructure.

If you do not understand this theory, you just need to keep in mind that the parameter $$t$$ can be related to the strength of the bond, therefore this approximation can give a quantitative strength of bonds relative to the overlap between orbitals. In the basic application of the theory, the Hamiltonian is made of 10 Slater-Koster (SK) hopping parameters between $$s, p$$ and $$d$$ orbitals : $$ss\sigma$$, $$sp\sigma$$, $$ss\sigma$$,$$pp\sigma$$, $$pp\pi$$, $$pd\sigma$$, $$pd\pi$$, $$dd\sigma$$, $$dd\pi$$, $$dd\delta$$. The strength of the SK parameters can give a quantitative approximation of the strength of the bond. I suppose that you are mainly interested in $$dd\sigma$$, $$dd\pi$$, $$dd\delta$$. These parameters can be obtained by a fit of a higher level of theory or experimental bandstructure if available. For a modeller, the values can be obtained easily, a reliable source is this book where some pages appears online. Another more complicated source is the NRL tight-bnding.

The sign of the SK parameters is not interesting for your question, only the magnitude matters : we will consider SK parameters as positive. For example, for Chromium (Cr) :

1. $$dd\sigma| \rightarrow 0.84$$ eV (81.46 kJ.mol$$^{-1}$$)
2. $$dd\pi \rightarrow 0.50$$ eV (48.22 kJ.mol$$^{-1}$$)
3. $$dd\delta \rightarrow 0.04$$ eV ( 3.51 kJ.mol$$^{-1}$$)

Obviously, the $$\sigma-$$bond is the strongest and the $$\delta-$$bond is the weakest bond formed but the overlap between two d-orbitals, about 10 times weaker than the $$\pi-$$bond. This result seems surprising maybe counterintuitive, but it is intuitive according to the picture above. The strength of a bond can be enhanced if the electron lies between the centers of the potential of the nucleus. An overlap has a coulomb cost reduces by the exchange interaction and more significantly by the potential of the nucleus if the overlap is not far from the nucleus : this is the case of a $$\sigma-$$bond. As shown in the figure above, in the case of $$d$$-orbital, the overlap $$dd\pi$$ is greater and has a $$\sigma$$ bond character but is simply farther from the nucleus : $$dd\pi < dd\sigma$$, however $$dd\pi \gg dd\delta$$ because of a planar overlap $$dd\delta$$.

The overlap $$dd\delta$$ is very similar to $$pp\pi$$, the only case where a $$\delta-$$bond can have more strength than a $$\pi-$$bond is when the $$\pi-$$bond between two $$p$$ orbitals.

Image source

• Interesting answer. I only have a technical note: please cite images the same way you would cite quoted text. Some images may require additional details if they are covered by specific licenses. Please keep that in mind. Jun 28, 2023 at 21:28
• You might also want to check out the mhchem package for MathJax. Specifically the \pu{...} macro for units. More help is on Chemistry Meta. Jun 28, 2023 at 21:32
• @Martin-マーチン got it! thanks. Jun 29, 2023 at 10:57