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The symmetry of the superconducting order parameter in quasi-two-dimensionalBEDT-TTF organic superconductors is a subject of ongoing debate. We report abinitio density functional theory calculations for a number of organicsuperconductors containing $\kappa$-type layers. Using projective Wannierfunctions we derive parameters of a common low-energy Hamiltonian based onindividual BEDT-TTF molecular orbitals. In a random phase approximationspin-fluctuation approach we investigate the evolution of the superconductingpairing symmetry within this model and point out a phase-transition betweenextended $s + d_{x^2-y^2}$ and $d_{xy}$ symmetry. We discuss the origin of themixed order parameter and the relation between the realistic moleculedescription and the widely used dimer approximation. Based on our ab initiocalculations we position the investigated materials in the obtained moleculemodel phase diagram and simulate scanning tunneling spectroscopy experimentsfor selected cases. Our calculations show that many $\kappa$-type materials lieclose to the phase transition line between the two pairing symmetry types foundin our calculation, possibly explaining the multitude of contradictoryexperiments in this field.

Near-degeneracy of extended $s + d_{x^2-y^2}$ and $d_{xy}$ order parameters in quasi-two-dimensional organic superconductors