Second-order Many-body Perturbation Theory Based The Screened Coulomb Interaction:Implementation And Applications To Molecular Systems

As the key issue in the field of condensed matter physics and computational chemistry,many-body interactions is the origin of abundant physical phenomenon.In terms of Green’s function,Hedin recast the many-body problem into a closed set of coupled integro-differential equations(Hedin’s equations)that need to be solved selfconsistently.In Hedin’s equations,the interactions between particles are described by the self-energy which is non-hermitian and energy-dependent.Due to its complexity in mathematics,Hedin proposed the GW approximation as the lowest-order approximation to the self-energy.Taking into account the screening effect,the GW approximation treats the electron with the surrounding medium as a quasiparticle.As the state-of-the art method in calculating the electronic excited-state properties of the system,the GW approximation gives proper description of energy bands and energy gaps in weakly-and moderately-correlated materials such as insulators and semiconductors,and its applications in the solid physics has undergone the development of more than half-century.In recent years,with the increasingly mature technique of localized basis and the development of algorithms,the GW method has gained more attention in the research area of finite systems such as molecules and clusters.However,scientists found that the GW method is faced with challenges in the descriptions of the fundamental gap of strongly-correlated systems such as transition-metal oxides,the ordering of certain energy levels in molecular systems,and its accuracy in predicting the photoemission spectrum of materials.Thereby,researchers have attempted to consider the inclusion of vertex correction to the self-energy and the polarisability to overcome the shortcomings of the GW method.The diagrammatic method that using Feynman diagrams to represent the self-energy and the polarizability,is one of the most important tools to include the vertex corrections in practical calculations.As the first-order diagram when expanding the self-energy in terms of the screened Coulomb interaction,the GW approximation completely ignores the contributions from the higher order Feynman diagrams which belong to vertex corrections.The main conclusions obtained from this paper are as follows:Firstly,based on the diagrammatic perturbation theory,for the first time we presented a parallel implementation of the full second-order self-energy(FSOS-W0)for finite systems in FHI-aims which is a software package for ab initio calculations.The diagrammatic correction we have implemented is exactly the second and the unique term of the perturbative expansions of the self-energy in terms of the screened Coulomb interaction.It turns out that the implementation obtains an approximate quintic-scaling with the system size,enabling calculations for systems with tens of atoms.Secondly,we assessed the performance of the FSOS-W0 correction in the GW100 testset and the Acceptor24 testset.These two sets consist closed-shell molecules belonging to different types but both mainly composed by the first three rows of the periodic table.The results show that the FSOS-W0 correction improve the description of the ionization energies and electron affinities of molecular systems significantly with respect to the G0W0 approach.Thirdly,we further enlarged the benchmark to 3d-transition metal monoxide(3dTMO)clusters with complex electronic structure,which are open-shell anions with highly-localized d-orbitals.It demonstrates that quasiparticle calculations including the FSOS-W0 correction(G0 W0Γ0(1))can give a proper description of the low-energy excitations of 3d-TMO anions.In addition,we found that,the best starting points for G0W0 and G0W0Γ0(1)calculations are different:G0W0 performs better based on starting points with more exact exchange(EXX)fraction to compensate its insufficiency in qualifying the correlation energy,while the situation for is the opposite.A further detailed analysis unveils that the EXX fraction of the best starting point for the G0 W0Γo(1)approach does not depend on the orbital nature and the case is different for G0 W0 calculations.However,the FSOS-W0 correction does have deficiencies,which are reflected in its difficulties in giving correct ordering and splittings between specific energy levels that have already been encountered in the G0W0 approach.