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We investigate low-temperature electronic states of the series of organicconductors $\beta^{\prime\prime}$-(BEDT-TTF)$_4$[(H$_3$O)M(C$_2$O$_4$)$_3$]G,where BEDT-TTF is bis(ethylenedithio)tetrathiafulvalene, and M and G representtrivalent metal ions and guest organic molecules, respectively. Our structuralanalyses reveal that the replacement of M and G give rise to systematic changein the cell parameters, especially in the $b$-axis length, which has positivecorrelation with the superconducting transition temperature $T_{\rm c}$.Analyses of temperature and magnetic field dependences of the electricalresistance including the Shubnikov-de Haas oscillations elucidates that thevariation of charge disproportionation, effective mass and the number ofitinerant carriers, can be systematically explained by the change of the$b$-axis length. The changes of the transfer integrals induced bystretching/compressing the $b$-axis are confirmed by the band calculation. Wediscuss that electron correlations in quarter-filled electronic bands lead tocharge disproportionation and the possibility of a novel pairing mechanism ofsuperconductivity mediated by charge degrees of freedom.

Effects of Electron Correlations and Chemical Pressures on Superconductivity of $\beta^{\prime\prime}$-type Organic Compounds