The fundamentals of peptide structure, such as hydrogen bonding and disulfide bridge formation were explored in the present first principle computational investigation along with point mutations. In this study, the consequences of changing the elements of molecular axis chirality in peptide dimerization have been analyzed by observing the interactions between the carboxyl-carboxyl hydrogen bonding between two free glycines. To further the appreciation of dimerizations, a model was built to study cystine. Cystine is formed when a disulfide bridge is formed between two cysteine residues. These dimerizations are known to help stabilize the secondary, tertiary and sometimes quaternary structure of the protein. Taking such observations into account, in order to understand biological phenomena in a first quantum mechanics sense, two models were built for point mutations. A substitution study of penta-alanine peptide model with subsequent replacement of central alanine by the other 19 amino acid residues, as well as a model of tri-peptide Pro-Glu-Glu to Pro-Val-Glu was analyzed. It should be noted that the later point mutation is particularly present in Sickle Cell ?-globin at the sixth position in the primary amino acid sequence. All calculations were done by first principle quantum mechanics using Hartree-Fock and DFT theory at 3-21G basis sets. The underlying objective of the present computational study was the geometry optimization of the peptide models for future study involving reaction mechanisms.