The possible involvement of chemical compounds in atmospheric new particle formation has received increased attention in recent years. Extensive density functional theory calculations were performed to characterize the effects of the inter- and intra-molecular hydrogen bonding interactions in forming atmospheric malonic acid (MOA)-containing clusters. Methanol, water, formaldehyde, and acetone are common atmospheric nucleation precursors, and they were chosen as the counterpart to interact with MOA. There are two types of hydrogen bonds: addition and insertion. When MOA behaves as the donor of a hydrogen bond, the formation of an inter-molecular hydrogen bond lightly increases the strength of the intra-molecular hydrogen bonds. Strong hydrogen bonds were formed when MOA executes as a hydrogen bond donor. The strength of the insertion conformer depends on the inserting molecule. The IR frequencies of the hydrogen bonded system were investigated. Furthermore, geometrically identified inter- and intra-molecular hydrogen bonds were provided by atoms in molecules approach.