# Bulletin of the American Physical Society

# APS March Meeting 2022

## Volume 67, Number 3

## Monday–Friday, March 14–18, 2022; Chicago

### Session K46: Excited State II: Method development-quantum embedding and X-ray Spectroscopy

3:00 PM–6:00 PM,
Tuesday, March 15, 2022

Room: McCormick Place W-470A

Sponsoring
Units:
DCOMP DMP

Chair: Sahar Sharifzadeh, Boston University

### Abstract: K46.00008 : Real-space Green's function approach for the Langreth cumulant*

4:48 PM–5:00 PM

#### Presenter:

John Rehr

(University of Washington)

#### Authors:

John Rehr

(University of Washington)

Joshua J Kas

(University of Washington)

*G*. As shown by Langreth, due to the linked-cluster theorem,

_{c}(t)*G*can be expressed exactly in cumulant form,

_{c}(t)*G*=

_{c}(t)*G*exp[C(t)], where the independent particle core-hole Green’s function is

_{c}^{0}(t)*G*and

_{c}^{0}=exp(iε_{c}t)*C(t)*is the cumulant. In an interacting electron system, the cumulant

*C(t)*is given to linear order by the density-response to a suddenly turned-on core-hole. In previous work, a real-time time-dependent density functional theory approach (RT-TDDFT) has been developed for the cumulant. Here we develop a real-space Green's function approach for the Langreth cumulant C(t). Our formulation starts from the observation that in frequency space, the cumulant kernel

*β(ω)*has the same form as the expression for the atomic polarizability in the TDDFT approach of Zangwill and Soven, but with the core-hole potential

*V(r)*replacing the dipole interaction. As a consequence, one can immediately derive a real-space Green's function approach, in analogy with the BSE-TDDFT formulation of Ankudinov et al. (TDDFT-BSE). In particular, the screened dipole matrix elements of XAS are replaced by screened monopole transition elements in response to a suddenly turned-on core-hole:

*M*, where the dynamically screened core-hole potential is

_{cL}= <c|V_{sc}|L>*V*(r) =

_{sc}*ε*, and the dielectric matrix is ε = [

^{-1}(ω) V_{c}(ω)*1-K*]. In contrast to XAS,

^{L}χ^{0}*V*and

_{c}(r)*V*are spherically symmetric, so the selection rules preserve angular momentum

_{sc}(r)*L=L*. Thus, the calculations with the RSGF approach are similar to XAS, except for modified matrix elements and selection rules. Also in analogy with the XAS, one can define a fine structure in the cumulant kernel due to near-neighbor scattering.

_{c}*This work is supported by DOE BES TCMP Grant No. DE-FG03-97ER45623

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