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We present the results of precise correlated-electron calculations on themonomer lattices of the organic charge-transfer solids $\kappa$-(BEDT-TTF)$_2$Xfor 32 and 64 molecular sites. Our calculations are for band parameterscorresponding to X = Cu[N(CN)$_2$]Cl and Cu$_2$(CN)$_3$, which aresemiconducting antiferromagnetic and quantum spin liquid, respectively, atambient pressure. We have performed our calculations for variable electrondensities $\rho$ per BEDT-TTF molecule, with $\rho$ ranging from 1 to 2. Wefind that $d$-wave superconducting pair-pair correlations are enhanced byelectron-electron interactions only for a narrow carrier concentration about$\rho=1.5$, which is precisely the carrier concentration wheresuperconductivity in the charge-transfer solids occurs. Our results indicatethat the enhancement in pair-pair correlations is not related toantiferromagnetic order, but to a proximate hidden spin-singlet state thatmanifests itself as a charge-ordered state in other charge-transfer solids.Long-range superconducting order does not appear to be present in the purelyelectronic model, suggesting that electron-phonon interactions also must play arole in a complete theory of superconductivity.

Coulomb enhancement of superconducting pair-pair correlations in a $\frac{3}{4}$-filled model for $\kappa$-(BEDT-TTF)$_2$X