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We report a $^{13}$C-NMR study on the ambient-pressure metallic phase of thelayered organic conductor $\theta$-(BEDT-TTF)$_{2}$I$_{3}$ [BEDT-TTF:bisethylenedithio-tetrathiafulvalene], which is expected to connect the physicsof correlated electrons and Dirac electrons under pressure. The orientationdependence of the NMR spectra shows that all BEDT-TTF molecules in the unitcell are to be seen equivalent from a microscopic point of view. This featureis consistent with the orthorhombic symmetry of the BEDT-TTF sublattice andalso indicates that the monoclinic $I_{3}$ sublattice, which should make threemolecules in the unit cell nonequivalent, is not practically influential on theelectronic state in the conducting BEDT-TTF layers at ambient pressure. Thereis no signature of charge disproportionation in opposition to most of the$\theta$-type BEDT-TTF salts.  The analyses of NMR Knight shift, $K$, and the nuclear spin-latticerelaxation rate, $1/T_{1}$, revealed that the degree of electron correlation,evaluated by the Korringa ratio [$\varpropto 1/(T_{1}TK^{2}$)], is in anintermediate regime. However, NMR relaxation rate $1/T_{1}$ is enhanced above$\sim$ 200K, which possibly indicates that the system enters into a quantumcritical regime of charge-order fluctuations as suggested theoretically.

Electron Correlations in the Quasi-Two-Dimensional Organic Conductor $\theta$-(BEDT-TTF)$_{2}$I$_{3}$ investigated by $^{13}$C NMR