Weak bonds such as hydrogen bond, pi-pi stacking and van der Waals interaction are much weaker in the strength but play a more important role for the existence of various lives. For example, they are the major intermolecular interactions in the liquid and solid structure of water and determine the 3 dimensional structure of protein and DNA, which are the crucial organic molecules in lives. As a result, studying these weak bonds can lead to the better understanding of fundamental knowledge of lives. Kohn-Sham (K-S) Density Functional Theory (DFT) is an accurate and effect way to investigate the fundamental properties for many-body systems, in which, only the exchange-correlation energy as a functional of electron density need to be approximated. However, weak interaction system is still a challenge problem for KS-DFT. In this dissertation work, several standard density functionals are used to study these weak interactions in the solid state structure ice as long as nucleic bases molecules in the biologic system. It is found that the hydrogen bond can be well described by most semilocal functionals: the mismatch problem of ice Ih and AgI for GGA functional can be solved by using the higher level meta-GGA functionals and the binding length and energy between nucleic bases in DNA can be well described. However, the more accurate dispersion correction is strongly needed for van der Waals interactions and pi stacking for super-high pressure ice phases and large size biologic molecules, where van der Waals interaction takes major role. Finally, the basic structural properties of various phases of ice and DNA can be understood based on the investigation with appropriate functionals. / acase@tulane.edu