Communication: Towards ab initio self-energy embedding theory in quantum chemistry

Abstract

The self-energy embedding theory (SEET), in which the active space self-energy is embedded in the self-energy obtained from a perturbative method treating the non-local correlation effects, was recently developed in our group. In SEET, the double counting problem does not appear and the accuracy can be improved either by increasing the perturbation order or by enlarging the active space. This method was first calibrated for the 2D Hubbard lattice showing promising results. In this paper, we report an extension of SEET to quantum chemical ab initio Hamiltonians for applications to molecular systems. The self-consistent second-order Green's function method is used to describe the non-local correlations, while the full configuration interaction method is carried out to capture strong correlation within the active space. Using few proof-of-concept examples, we show that SEET yields results of comparable quality to n-electron valence state second-order perturbation theory with the same active space, and furthermore, the full active space can be split into smaller active spaces without further implementation. Moreover, SEET avoids intruder states and does not require any high-order reduced density matrices. These advantages show that SEET is a promising method to describe physical and chemical properties of challenging molecules requiring large active spaces.

Efficient Temperature-Dependent Green’s Function Methods for Realistic Systems: Using Cubic Spline Interpolation to Approximate Matsubara Green’s Functions

“…Methods such as the random phase approximation (RPA) and GW usually express the Green's function using real frequencies to obtain spectra at zero temperature [37,38]. While, in general, the real frequency Green's function is an exponentially decaying function of frequency, it is very difficult to employ it in iterative methods such as DMFT or other embedding methods such as self-energy embedding theory (SEET) [39,40] since iterating usually requires pole shifting algorithms [41][42][43].…”

Dynamical screening in correlated electron systems—from lattice models to realistic materials

“…Therefore, non-locality is included at the GW level, and the method can be applied to study first-principles Hamiltonians. Different schemes along these lines have become popular also in other contexts, such as in quantum chemistry [11][12][13], where the quantum system is divided into two parts, one of which is treated at the perturbative level, e. g. by the self-consistent second-order Green's function method (GF2), while the other is solved at a higher level by the configuration interaction (CI) method [14,15]. However, what distinguishes GW+DMFT from other approaches is the double embedding in both the Green's function G and the dynamically screened interaction W .…”

“…(13). The DMFT approximation is the identification of the lattice self-energy with the momentum-independent impurity self-energy,…”

Periodic and fragment models based on the local correlation approach

“…One of the simplest embedding schemes of the first kind is point‐charge electrostatic embedding, where the cluster is placed inside a matrix of point charges. For higher accuracy, however, such a simple scheme is in many cases not sufficient, and various more elaborate embedding approaches have been proposed (Beran & Nanda, ; Birkenheuer, Fulde, & Stoll, ; Bygrave, Allan, & Manby, ; Fornace, Lee, Miyamoto, Manby, & III, ; Herschend, Baudin, & Hermansson, ; Huang, Pavone, & Carter, ; Knizia & Chan, , ; Lan, Kananenka, & Zgid, ; Manby, Stella, Goodpaster, & III, ; Masur, Schütz, Maschio, & Usvyat, ; Müller & Hermansson, ; Müller & Usvyat, ; Müller, Usvyat, & Stoll, ; Sode, Keçili, Yagi, & Hirata, ; Taylor, Bygrave, Hart, Allan, & Manby, ; Wen, Nanda, Huanga, & Beran, ).…”