The interactions of proteins, polysaccharides and other biomolecules with Ca(2+), CO3(2-), and water are central to the understanding of biomineralization and crystallization of calcium carbonate (CaCO3), and their association with the natural organic matter (NOM) in the environment. A molecular-level investigation of how such interactions and thermodynamic forces drive the nucleation and growth of crystalline CaCO3 in living organisms remains elusive. This paper presents ab initio and metadynamics studies of the interactions of Ca(2+), CO3(2-), and water with the essential amino acids/functional groups, e.g. arginine/NH2(+), aspartate or glutamate/COO(-), aspartic or glutamic acid/COOH, and serine/OH, of protein/organic molecules that are likely to be critical to the biomineralization of CaCO3. These functional groups were modeled as guanidinium (Gdm(+)), acetate (AcO(-)), acetic acid (AcOH), and ethanol (EtOH) molecules, respectively. The Gdm(+)-Ca(2+)-CO3(2-) and AcO(-)-Ca(2+)-CO3(2-) systems were found to form stable ion-complexes irrespective of the presence of near neighbor water molecules. The strong electrostatic interactions of these functional groups with their counter-ions significantly affect the fundamental vibrational frequencies of the functional groups, mainly the NH2 stretching (str.) and degenerate (deg.) scissors modes of Gdm(+) and -C=OO, CC, and CO str. modes of AcO(-). The free-energy calculations reveal that EtOH forms weakly bound molecular complexes with the Ca(2+)-CO3(2-) ion pairs in water. However, the interaction strength of EtOH with crystalline CaCO3 can increase significantly due to combined effect of H-bond and electron donor acceptor (EDA) type of interactions. These results indicate that -NH2(+) and -COO(-) bearing molecules serve as potential nucleation sites promoting crystallization of CaCO3 phases while -OH bearing molecules are likely to control the morphology of the crystalline phases by attaching to the growing crystal surfaces.