  We present the results of precise correlated-electron calculations on the
monomer lattices of the organic charge-transfer solids $\kappa$-(BEDT-TTF)$_2$X
for 32 and 64 molecular sites. Our calculations are for band parameters
corresponding to X = Cu[N(CN)$_2$]Cl and Cu$_2$(CN)$_3$, which are
semiconducting antiferromagnetic and quantum spin liquid, respectively, at
ambient pressure. We have performed our calculations for variable electron
densities $\rho$ per BEDT-TTF molecule, with $\rho$ ranging from 1 to 2. We
find that $d$-wave superconducting pair-pair correlations are enhanced by
electron-electron interactions only for a narrow carrier concentration about
$\rho=1.5$, which is precisely the carrier concentration where
superconductivity in the charge-transfer solids occurs. Our results indicate
that the enhancement in pair-pair correlations is not related to
antiferromagnetic order, but to a proximate hidden spin-singlet state that
manifests itself as a charge-ordered state in other charge-transfer solids.
Long-range superconducting order does not appear to be present in the purely
electronic model, suggesting that electron-phonon interactions also must play a
role in a complete theory of superconductivity.
