What would follow in the series sigma, pi and delta bonds?

I realise, that this question is a stretch, but I was wondering, how would a bonding orbital be called if it was formed from two $f\_{x(x^2−3y^2)}$ or $f\_{y(3x^2−y^2)}$ orbitals. Have there been any suggestions on this, was it anywhere proposed or discussed? I am not arguing about the existence of such a thing, but as a thought experiment, how would it be called? Phi, $\varphi$?


I am also throwing in a reference request here, since I am interested in any literature related to the topic.


Some background: 


* A $\sigma$ orbital is an orbital, that has no nodal plane between the bonding partners. It is $C\_\infty$ symmetric with respect to the bonding axis (in first approximation - of course $d\_{xy}$ orbitals can align in a $\sigma$ fashion, too, but for the sake of the argument, let's not consider this.) The point group of this orbital can further be assumed as $D\_\mathrm{\infty h}$. It shares therefore most features of an $s$ orbital, hence $s$igma, $\sigma$.  

The most prominent example for this is probably the dihydrogen, $\ce{H2}$, molecule.
* A $\pi$ orbital has one nodal plane and the bonding axis of the involved atoms is part of this plane. It is therefore asymmetric, $C\_1$, with respect to this plane. However, it is $C\_\mathrm{s}$ symmetric with respect to the plane that is perpendicular, also sharing the bonding axis. The orbital has further the point group $C\_\mathrm{2v}$. It has therefore most features of a $p$ orbital, hence $p$i, $\pi$.  

The most prominent examples for $\pi$ bonds are probably ethylene, $\ce{C2H4}$, and acetylene, $\ce{C2H2}$.
* A $\delta$ orbital has two nodal planes between the bonding partners. These are perpendicular to each other. The bond orbital is asymmetric with respect to both of them. As a result, it is $C\_\mathrm{s}$ symmetric with respect to the bisecting mirror planes. The point group of this orbital is $D\_\mathrm{2h}$. Therefore it has shares features with a $d$ orbital, hence $d$elta, $\delta$.  

One example is the $\ce{[Re2Cl8]^{2-}}$ ion, see [Wikipedia's quadruple bond](http://en.wikipedia.org/wiki/Quadruple_bond).
* I imagine two $f$ orbitals aligning with the bonding axis being simultaneously a $C\_3$ symmetry axis, giving it an overall $D\_\mathrm{3h}$ point group. Since there is no greek letter starting with an $f$, I think the logical thing would be to choose $\phi$ as it sounds a like. (I cannot be the only one thinking that.)


The following graphic should somewhat demonstrate what I mean:  

![sigma, pi, delta, and phi (?) linear combinations](https://i.stack.imgur.com/El7QH.jpg)


I have to admit, that I have not done much research about this. It was more like an impulsive question for me to ask.




**tl;dr** The next in the series is called φ bond. There is even a tiny [Wikipedia article](http://en.wikipedia.org/wiki/Phi_bond) about it.




---


Nicolau pointed me to the [Wikipedia article](http://en.wikipedia.org/wiki/Molecular_orbital#.CF.86_symmetry), that had at the time a tiny section about the φ symmetry of the bond. Ben also kindly agreed with my naming proposition. I'd like to back up just a little bit an quote one sentence of this article:



> 
> The type of interaction between atomic orbitals can be further categorized by the molecular-orbital symmetry labels σ (sigma), π (pi), δ (delta), φ (phi), γ (gamma) etc. paralleling the symmetry of the atomic orbitals s, p, d, f and g. The number of nodal planes containing the internuclear axis between the atoms concerned is zero for σ MOs, one for π, two for δ, etc.
> 
> 
> 


Basically this was what I was already thinking, but since the section is quite tiny overlooked it accordingly. But since this is a reference request, I'll go a little deeper. 


The concept of the bond is actually quite old and I was able to track it down to at least 1984, where Bruce E. Bursten and Geoffrey A. Ozin "demonstrate[d] for the first time the existance of φ bonds between metal atoms."[1] A little further back, 1978, N. Rösch and A. Streitwieser already performed SCF-Xα calculations on thorocene and uranocene, where they came across f orbital contributions in bonding. Yet, they did not coin the phrase φ bond.[2] Following that, there have been more theoretical studies on the diuranium molecule, with increasing level of theory.[3] One of the more recent studies is by Laura Gagliardi and Björn O. Roos, which is available free of charge (see below).[4] Xin Wu and Xin Lu also studied the phenomenon in endohedral matallofullerenes, i.e. diuranium in a Buckminster fullerene.[5]


It is quite safe to assume, that there are more studies about this research topic or in a more general aspect the research on molecules with high bond orders. For this purpose I will include a couple of good reads.[6]


**References and further reading**


1. [Bruce E. Bursten, Geoffrey A. Ozin, *Inorg. Chem.*, **1984**, *23* (18), 2910–2911.](http://pubs.acs.org/doi/abs/10.1021/ic00186a039)
2. (a) [Rösch, N., Streitwieser, A., Jr., *J. Organomet. Chem.*, **1978**, *115*, 195-200.](http://dx.doi.org/10.1016/S0022-328X(00)91124-0) (b) [Rösch, N., Streitwieser, A., Jr., *J. Am. Chem. Soc.* **1983**, *105*, 7237-40.](http://pubs.acs.org/doi/abs/10.1021/ja00363a004)
3. [Melanie Pepper, Bruce E. Bursten, *J. Am. Chem. Soc.*, **1990**, *112* (21), 7803–7804.](http://pubs.acs.org/doi/abs/10.1021/ja00177a055)
4. [Laura Gagliardi, Björn O. Roos, *Nature*, **2005**, *433*, 848-851.](http://dx.doi.org/10.1038/nature03249) Available free at [Archive ouverte UNIGE](http://archive-ouverte.unige.ch/unige:3652).
5. [Xin Wu, Xin Lu, *J. Am. Chem. Soc.*, **2007**, *129* (7), 2171–2177.](http://pubs.acs.org/doi/abs/10.1021/ja067281g)
6. Without order: (a) [Gernot Frenking, *Nature*, **2007**, *446*, 276-277.](http://www.nature.com/nature/journal/v446/n7133/full/446276a.html)
(b) [Gernot Frenking, *Science*, **2005**, *310*, 796-797.](http://www.sciencemag.org/content/310/5749/796)
(c) [Gabriel Merino, Kelling J. Donald, Jason S. D'Acchioli, Roald Hoffmann, *J. Am. Chem. Soc.*, **2007**, *129* (49), 15295–15302.](http://pubs.acs.org/doi/abs/10.1021/ja075454b)
(d) [Fernando Ruipérez, Gabriel Merino, Jesus M. Ugalde, Ivan Infante, *Inorg. Chem.*, **2013**, *52* (6), 2838–2843.](http://pubs.acs.org/doi/abs/10.1021/ic301657c)
(e) [Jia Zhou, Jason L. Sonnenberg, H. Bernhard Schlegel, *Inorg. Chem.*, **2010**, *49* (14), 6545–6551.](http://pubs.acs.org/doi/abs/10.1021/ic100427t)
(f) [Awal Noor, Rhett Kempe, *Inorg. Cimica Acta*, **2015**, 424, 75-82.](http://dx.doi.org/10.1016/j.ica.2014.08.030)
(g) [Frank R. Wagner, Awal Noor, Rhett Kempe, *Nature Chemistry*, **2009**, *1*, 529-536.](http://www.nature.com/nchem/journal/v1/n7/full/nchem.359.html)
(h) [Björn O. Roos, Antonio C. Borin, Laura Gagliardi, *Angew. Chem. Int. Ed.*, **2007**, *46* (9). 1469-1472.](http://onlinelibrary.wiley.com/doi/10.1002/anie.200603600/abstract)


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