MP2/6-31++G(d,p) and DFT B3LYP/6-31++G(d,p) calculations were performed of the structure, binding energies, and vibrational modes of complexes between dimethyl sulfoxide (DMSO) as a proton acceptor and monoprotic linear acids HX (X = F, Cl, CN) as well as monoprotic carboxylic acids HOOCR (R = -H, -CH3, -C6H5) in 1:1 and 1:2 stoichiometric ratios. The results show that two different structures are possible in the 1:2 ratio: in the first, the DMSO molecule interacts with both acid molecules (leading to a "Y" structure); in the second, the DMSO interacts with only one monoprotic acid. The second structure shows a lower stability per hydrogen bond. The spontaneities of the reactions to form the 1:1 and 1:2 complexes are greatly influenced by the X group of the linear acid. With the exception of HCN, all the reactions are spontaneous. In the 1:2 complexes with Y structure, we observed that the hydrogen atoms of the linear acid are coupled in symmetric and asymmetric modes, while this type of coupling is absent from the other 1:2 complexes.