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The charge transfer compound (BEDT-TTF)$_2$Ag(CF$_3$)$_4$(TCE) crystallizesin three polymorphs with different alternating layers: While a phase with a$\kappa$ packing motif has a low superconducting transition temperature of$T_c=2.6$ K, two phases with higher $T_c$ of $9.5$ and $11$ K are multi-layeredstructures consisting of $\alpha'$ and $\kappa$ layers. We investigate thesethree systems within density functional theory and find that the $\alpha'$layer shows different degrees of charge order for the two $\kappa$-$\alpha'$systems and directly influences the electronic behavior of the conducting$\kappa$ layer. We discuss the origin of the distinct behavior of the threepolymorphs and propose a minimal tight-binding Hamiltonian for the descriptionof these systems based on projective molecular Wannier functions.

Role of layer packing for the electronic properties of the organic superconductor (BEDT-TTF)$_2$Ag(CF$_3$)$_4$(TCE)