What would follow in the series sigma, pi and delta bonds?
tl;dr The next in the series is called &phi; bond. There is even a tiny Wikipedia article about it.



Nicolau pointed me to the Wikipedia article, that had at the time a tiny section about the &phi; 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 &sigma; (sigma), &pi; (pi), &delta; (delta), &phi; (phi), &gamma; (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 &sigma; MOs, one for &pi;, two for &delta;, 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 &phi; bonds between metal atoms."[1] A little further back, 1978, N. Rösch and A. Streitwieser already performed SCF-X&alpha; calculations on thorocene and uranocene, where they came across f orbital contributions in bonding. Yet, they did not coin the phrase &phi; 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


Bruce E. Bursten, Geoffrey A. Ozin, Inorg. Chem., 1984, 23 (18), 2910–2911.
(a) Rösch, N., Streitwieser, A., Jr., J. Organomet. Chem., 1978, 115, 195-200. (b) Rösch, N., Streitwieser, A., Jr., J. Am. Chem. Soc. 1983, 105, 7237-40.
Melanie Pepper, Bruce E. Bursten, J. Am. Chem. Soc., 1990, 112 (21),  7803–7804.
Laura Gagliardi, Björn O. Roos, Nature, 2005, 433, 848-851. Available free at Archive ouverte UNIGE.
Xin Wu, Xin Lu, J. Am. Chem. Soc., 2007, 129 (7), 2171–2177.
Without order: (a) Gernot Frenking, Nature, 2007, 446, 276-277.
(b) Gernot Frenking, Science, 2005, 310, 796-797.
(c) Gabriel Merino, Kelling J. Donald, Jason S. D'Acchioli, Roald Hoffmann, J. Am. Chem. Soc., 2007, 129 (49), 15295–15302.
(d) Fernando Ruipérez, Gabriel Merino, Jesus M. Ugalde, Ivan Infante, Inorg. Chem., 2013, 52 (6), 2838–2843.
(e) Jia Zhou, Jason L. Sonnenberg, H. Bernhard Schlegel, Inorg. Chem., 2010, 49 (14), 6545–6551.
(f) Awal Noor, Rhett Kempe, Inorg. Cimica Acta, 2015, 424, 75-82.
(g) Frank R. Wagner, Awal Noor, Rhett Kempe, Nature Chemistry, 2009, 1, 529-536.
(h) Björn O. Roos, Antonio C. Borin, Laura Gagliardi, Angew. Chem. Int. Ed., 2007, 46 (9). 1469-1472.