Works done during this thesis split into two main themes, themselves subdivided in several projects. On the one hand, works have been led concerning the analysis and the development of double-hybrid functionals. An analysis of linearly-separated double-hybrid functionals along the adiabatic connection has been proposed. A new range-separated double-hybrid functional based on an alternative separation of the exchange-correlation energy, RSDHf, has been developed. On the other hand, works related to the development of analytic potential energy surfaces (PES) has been led. A new analytic potential has been proposed for the description of the PES of triatomic systems. The combinaition of this potential with an electrostatic potential has been used for the development of analytic PES for small systems in weak interaction : H2O···HF, HF2-, Ne···ClF.
Quantum study of strong and weak interactions : development of double-hybrid functionals and of analytic potential surfaces