The critical temperature ( ) of superconductivity in compounds is generally lower smaller with alkali atoms (A). Furthermore decreases with applied pressure. In the BCS model, these trends are explained by the lower density of states at the Fermi level for a decreased lattice constant (R). There is more than one counterexample, however, suggesting that BCS does not give the whole truth. The most important one is that the compound with the largest lattice constant, , is not superconducting at all at ambient pressure. In this paper we derive a novel model where a negative lattice contribution to Hubbard U, proportional to 1/R, is taken into account. It is possible to explain why compounds with A = Li, and Na have a low or are not superconducting at all, and why is superconducting only at applied pressure and then with the highest of all alkali fullerides. It is concluded that the density of states mechanism derived in the BCS model is in doubt. Nevertheless superconductivity in depends on electron-phonon coupling. The dominating phonon is the bond stretching phonon, a breathing phonon for the whole fullerene molecular ion. 1. Introduction The discoveries of conductivity and superconductivity (SC) in and were great events in science during the 1990s [1–5]. SC was later discovered in a number of other compounds, where A stand for alkali atoms: Li, Na, K, Rb, or Cs. Generally, increase of the lattice constant leads to a higher critical temperature . Some of the compounds (A = Li, Na) with the smallest lattice constants are not superconducting [6–8]. Only fullerides have proven to be superconducting (SC). Remarkably, the compound with the highest lattice constant does not follow this trend [9–11]. Disorder-free is an antiferromagnetic insulator at ambient pressure. However, already at the quite modest pressure of 3？kbar ( 3000？atm), it turns into a superconductor (SC) with the highest known for any fulleride [9–11]. At temperatures above passes directly into a semiconducting and antiferromagnetic phase. This system thus needs an explanation model which is not depending on the existence of free electrons, as in the BCS model. Takabayashi et al. further point out  that transfer from SC to antiferromagnetic phase appears to be “purely electronic”, thus seemingly explicable without resorting to nuclear dynamics. There are a number of peculiarities in experimental data in general, as summarized by Gunnarsson , Rosseinsky , Margadonna and Prassides , and Iwasa and Takenobu . A widely accepted approach is to treat the metallic alkali fullerides
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