We report on Shubnikov-de Haas and de Haas-van Alphen measurements of an or
ganic metal based on the molecular donor bis(ethylenedioxy)-tetrathiavulval
ene (= BEDO-TTF) and the anion Cl<SUP>-</SUP> with H<INF>2</INF>O molecules
. The observed single oscillation frequency perfectly follows the two-dimen
sional dependence F = F<INF>0</INF>/cos Theta with F<INF>0</INF> = (4890 +/
- 20) T. The Fermi-surface area of similar to 50% of the first Brillouin zo
ne proves a quarter-filled band, i.e., a 2:1 stoichiometry of the BEDO-TTF
donor with respect to the anion. The apparent discrepancy to X-ray data whi
ch give a 1:1<SUP></SUP> ratio between BEDO-TTF and Cl<SUP>-</SUP> is under
stood by replacement of H<INF>2</INF>O molecules with (H<INF>3</INF>O)<SUP>
+</SUP> ions. The proposed stoichiometry therefore is (BEDO-TTF)<INF>2</INF
><SUP>+</SUP> (H<INF>5</INF>O<INF>2</INF>)<SUP>+</SUP>(Cl<SUP>-</SUP>)<INF>
2</INF>. The cyclotron effective mass is m<INF>c</INF> (1.54 +/- 0.05)m<INF
>e</INF>/cos Theta when deduced from the temperature dependence of the fund
amental oscillation amplitude, but strongly reduced when extracted from hig
her harmonics. This and the strong harmonic content of the oscillations sig
nals an influence of the two-dimensional electronic structure and can by qu
alitatively understood by applying the concept of magnetic interaction to t
he effect of the oscillatory chemical potential.