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In sharp contrast with the hydrogen bond, which has beenwell established to be one of the strongest interactions between two atomic and/or molecular species, weak interactions between two closed-shell molecules have not been understood in detail. We have thus carried out a systematic study on complexes shown in the title; examples include the CO-ethylene oxide (EO), CO-ethylene sulfide (ES), CO-dimethyl ether (DME), CO-dimehtyl sulfide (DMS), CO$2$-EO, CO$2$-ES, CO$2$-DME, and CO$2$-propylene oxide (PO) complexes. From their Fourier transform microwave spectra, we determined the $rs$ structure, the force constant of the van der Waals stretching mode, and the dissociation energy by analyzing the observed rotational and centrifugal distortion constants. We have also carried out ab initio molecular orbital calculations at the level of MP2 with basis sets 6-311++G($d,p$) and aug-cc-pVDZ using the Gaussian 09 package. In most cases, the MP2/6-311++G($d,p$) calculations yield rotational constants in better agreement with the experimental values, than the other basis set, in other word, the molecular structures calculated using this basis set are close to those experimentally found for the ground state. The estimated bond dissociation energies including the zero-point vibrational energy corrections $\Delta$ZPV and the basis set superposition errors (BSSE) calculated with the counterpoise correction (CP) are in good agreement with the observed binding energies $EB$. We have applied an NBO analysis to the complexes to calculate the stabilization energy CT (= $\Delta$), which we found are closely correlated with the binding energies $EB$. We have thus achieved a consistent overview on the intermolecular interaction in the complexes under consideration.