Particle-Particle RPA And The RPA Gradient Within The Numerical Atomic Orbital Framework

The first-principle methods are used to calculate the ground-state energy of many-electron systems,where the exchange-correlation part of total energy is approximated.The random phase approximation(RPA)is one of the method for computing the ground-state correlation energy.In this thesis,we present a comparative study of particle-hole and particle-particle channels of RPA for molecular dissociations of different bonding types.We introduced a direct particle-particle RPA scheme,in analogy to the direct particle-hole RPA formalism,whereby the exchange-type contributions are excluded.This allows us to compare the behavior of the particle-hole and particle-particle RPA channels on the same footing.Our study unravels the critical role of exchange contributions in determining behaviors of the two RPA channels for describing stretched molecules.We also made an attempt to merge particle-hole RPA and particle-particle RPA into a unified scheme,with the double-counting terms removed.However,benchmark calculations indicate that a straightforward combination of the two RPA channels does not lead to a successful computational scheme for describing molecular dissociations.We then describe an implementation of the exact-exchange optimized effective potential(OEP)method within the numeric atom-centered orbital(NAO)framework.The products of occupied and unoccupied atomic orbitals are used as the auxiliary basis to solve the OEP equations,which connects the response function and the local Kohn-Sham(KS)potential.This will help us to o’btain stable solution for OEP calculations by making connection between local and non-local exchange potential,from which a local exact-exchange potential is determined.The role of different finite basis set is studied for stable OEP calculations.We have also extended the exact exchange OEP method to RPA correlation by considering OEP correlation potential based on d-phRPA correlation in context of optimized effective potential.Finally we present the implementation details for calculating the RPA gradient within the NAO framework.Our implementation allows to relax the geometries of molecules according to the RPA force.We provide test results for the bond lengths for a few small molecules.The RPA geometry is then compared to those obtained by other electronic structure methods.